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Q&A for How to Solve Simultaneous Equations Graphically
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QuestionWhat will be the answer if lines do not intersect?DonaganTop AnswererIf the graphed lines do not intersect, the system has no solution. That means there is no set of values for the variables that will work for both equations simultaneously.
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QuestionHow do I guess the number, like x=0 or x=1, etc.?DonaganTop AnswererYou don't guess any numbers. You simply use a low number for x (like 0, 1, 2, -1, or -2, for example) so that it's easy to calculate the corresponding value of y.
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QuestionHow do I solve y=2x+1, y=x-5?DonaganTop AnswererPlot both equations on the same graph. The x and y values of the point where the two lines intersect are the solution of the equations.
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QuestionWhy do we take 0 as the value of x?DonaganTop AnswererChoosing zero for the value of x simply makes it easier and quicker to find the corresponding value of y, which would be the y-intersect.
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QuestionHow do I plot 3x + 7y = 13 graphically?DonaganTop AnswererFirst algebraically solve for y in terms of x (or vice versa). Then assign convenient values to x, and calculate corresponding values of y. Then plot some pairs of values (at least two pairs for a straight-line graph; more than two for a curved-line graph), and draw the graph. (You can graphically find the value of one variable when zero is assigned as the value of the other variable by simply noticing where the graph crosses each of the axes.)
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QuestionIs it possible that the two lines plotted on the graph will meet, and what happens if they don't meet?DonaganTop AnswererAll non-parallel lines (in the same plane) will meet somewhere. Two lines that are parallel to each other will not meet. That means that they have the same slope. In that case the two equations are not solvable.
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QuestionIs 2x-5y=32, 2x+3y=0 solvable using this method?Community AnswerYes. Any "linear" equations like these (meaning relatively simple equations) are solvable this way. The one exception occurs when the equations graph as parallel lines, in which case the lines don't intersect.
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QuestionIf we plot a different value of y, then find the value of x, will it be the same answer?DonaganTop AnswererYes. It doesn't matter what values are used in plotting the lines. Once plotted, they will intersect in one point only (assuming straight lines) regardless of the values used, and the point of intersection is the solution to the problem.
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QuestionWhat is the graph answer to y=x+1, y=7-x?DonaganTop AnswererBy plotting each of those equations, you will get two straight lines which intersect at the point (3,4). That means that both equations are true when x=3 and y=4. Graphically, the solution to this system of equations is (3,4).
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QuestionWhere did 18 and -8 come from?DonaganTop Answerer18 and -8 are the x- and y-coordinates, respectively, of the point of intersection of the two lines in the example graph.
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QuestionHow do I solve 2x + y = 3, x - 3y = 1?DonaganTop AnswererTo solve that system graphically: First solve each equation for x in terms of y, or y in terms of x (it doesn't matter which). Then make two tables of values (one for each equation) by assigning convenient values to the independent variable and calculating the corresponding values for the dependent variable. (For example, solve the second equation x: x = 3y + 1. Here y is the independent variable, and x is the dependent variable. Assign small values to y, and find the corresponding values for x. Then plot a line for each equation using at least two pairs of values for each. Both will be straight lines. The system's solution consists of the coordinates of the lines' point of intersection.
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QuestionHow do I solve x + y = -1 and 2x + y = 5?DonaganTop AnswererFirst re-write each equation to set y equal to an expression in x (or vice versa). (In this case, y = -1 - x, and y = 5 - 2x.) Then you can solve the system graphically (as shown above) or algebraically (by substitution or elimination).
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QuestionHow do I plot 1/3 on a graph?DonaganTop AnswererIf x = 1/3, plot it as a vertical line crossing the x-axis at +1/3. If y = 1/3, plot it as a horizontal line crossing the y-axis at +1/3.
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QuestionWhere did you get 18,-8?DonaganTop AnswererThat is the physical point of intersection on the graph, determined simply by inspecting the lines drawn on the graph. Those lines intersect at the one point on the graph where x = +18 and y = -8.
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QuestionSolve 2x²+3x+2=0 and -2x²-8x-5=3?DonaganTop AnswererSolve by the elimination method. (You make that choice by noticing that one of the equations has the term +2x², while the other equation has the term -2x².) By adding the two equations together, the x² terms cancel (or "eliminate") each other. Then all that's left is the relatively easy task of solving for x.
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QuestionCan you just make the equations into linear general form rather than substuite 0?DonaganTop AnswererYes, you can (assuming the equations are already linear), but substituting zero is a really easy method.
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QuestionHow the table for x and y is made how we will decide their value if it different from the book will graph be the same?DonaganTop AnswererIt doesn't matter which values you choose for x (or the independent variable). If you perform the calculations correctly, you'll get the appropriate corresponding values of y (or the dependent variable), and the graph will be correct.
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QuestionHow do I solve equation using powers?DonaganTop AnswererGraph each equation on the same grid. The point or points of intersection of the two graphed lines will be the solution(s) expressed as values of x and y. (If the lines don't intersect, there is no solution.)
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QuestionHow do I solve x + y = 4, and x - y = 6 graphically?Community AnswerThis is a relatively simple exercise. Solve for y in terms of x in both equations. Then plot the two straight lines corresponding to the equations. Look closely at the point of intersection of the two lines. The x- and y-coordinates of that point are the x- and y-values you're looking for.
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QuestionSolve the equation graphically x+y=5 and x+y=2.Community AnswerThose two equations would be represented by parallel lines on a graph. So the lines would never intersect, and there is no solution to that system. In other words, there are no values of x and y that would satisfy both equations simultaneously.
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QuestionWhat is x + 18 + 14 = 14?I_l1ke_gam3sCommunity AnswerFirst combine the like terms. x + 32 = 14. Then subtract 32 on both sides, leaving you with + x = 14 - 32. 14 - 32 = - 18. So x = -18.
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QuestionHow do I solve y - 2x = -1, and y + x = 5?Community AnswerEither follow the instructions above, or use the elimination method, which is relatively simple in this case: First subtract either equation from the other in order to get rid of the y terms. For example, subtract the first equation from the second to find that x = 2. Plug that x-value into either original equation to find that y = 3.
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Questionhow do I solve x+y=4, and x-y=2?Community AnswerIt's easiest to use the elimination method: Add these two equations together. You get 2x = 6, and x = 3. Plug that x-value into either original equation, and you find that y = 1.
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QuestionSolve 3x-y=4 and x+2y=6 algebraically.Community AnswerUse the elimination method (often the easiest method): first multiply the first equation by 2 to get 6x - 2y = 8. Then add that equation to the second original equation in order to eliminate the y-terms: 7x = 14, and x = 2. Plug that x-value into either original equation to solve for y: 3(2) - y = 4, so 6 - y = 4, and y = 2. Both x and y equal 2.
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QuestionHow do I solve the simultaneous equations graphically: 6r+5s=8; 4r+s=3?Community AnswerFirst set up a graph with r and s axes (instead of x and y). Then solve both equations for r in terms of s. (If you prefer, you could solve for s in terms of r.) Now create a table of values with corresponding values of r and s (as you would with x and y). Then draw a graph of the two lines representing the equations. The r- and s-coordinates of the point of intersection of the two lines are the r- and s-values you're looking for.
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QuestionHow to solve y=2x2-3x-5 and 2y=2x+11 if the graph isn't perfect?DonaganTop AnswererIf you're worried about the accuracy of the graphing, you could solve the simultaneous equations algebraically. See Solve Simultaneous Equations Using Elimination Method , Solve Simultaneous Equations Using Substitution Method and related articles.
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QuestionThe thing is I understand this but when it comes to the table, I am confused like how am I supposed to know which values to put at X?DonaganTop AnswererJust select two or more small values of x (positive or negative), and then solve the equation for the corresponding values of y. For example, select +1 for the value of x, and solve the equation to see what y would be when x is +1. Do that with two (or more) x/y combinations for a linear (straight line) equation and three (or more) x/y combinations for a quadratic (curved-line) equation. You can choose any x values you want. Choosing small x values makes finding the corresponding y values easier.
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QuestionHow do I know X and Y values if replaced with other alphabets like D or A?DonaganTop AnswererIn that case, you would not use x- and y-axes. You would use d- and a-axes, and then proceed in the same way. (Plot the independent variable -- x in the usual case -- on the horizontal axis and the dependent variable -- typically y -- on the vertical axis.)
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QuestionHow do we make the table?DonaganTop AnswererChoose convenient (small) values for the independent variable (typically x), and calculate the corresponding values of the dependent variable (typically y). Make a table with x and y columns, and place your pairs of x and y values in the columns.
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QuestionHow to calculate my points to graph y=x²+2x-3 and y=8-2x-x² as simultaneous equations?DonaganTop AnswererChoose convenient values of x, and calculate the corresponding values of y. For example, in the first equation, if x=1, y=0. If x= -1, y= -4. Plot several points for each equation.
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