Q&A for How to Solve Simultaneous Equations Graphically

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  • Question
    What will be the answer if lines do not intersect?
    Donagan
    Top Answerer
    If 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.
  • Question
    How do I guess the number, like x=0 or x=1, etc.?
    Donagan
    Top Answerer
    You 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.
  • Question
    How do I solve y=2x+1, y=x-5?
    Donagan
    Top Answerer
    Plot 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.
  • Question
    Why do we take 0 as the value of x?
    Donagan
    Top Answerer
    Choosing 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.
  • Question
    How do I plot 3x + 7y = 13 graphically?
    Donagan
    Top Answerer
    First 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.)
  • Question
    Is it possible that the two lines plotted on the graph will meet, and what happens if they don't meet?
    Donagan
    Top Answerer
    All 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.
  • Question
    Is 2x-5y=32, 2x+3y=0 solvable using this method?
    Community Answer
    Yes. 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.
  • Question
    If we plot a different value of y, then find the value of x, will it be the same answer?
    Donagan
    Top Answerer
    Yes. 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.
  • Question
    What is the graph answer to y=x+1, y=7-x?
    Donagan
    Top Answerer
    By 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).
  • Question
    Where did 18 and -8 come from?
    Donagan
    Top Answerer
    18 and -8 are the x- and y-coordinates, respectively, of the point of intersection of the two lines in the example graph.
  • Question
    How do I solve 2x + y = 3, x - 3y = 1?
    Donagan
    Top Answerer
    To 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.
  • Question
    How do I solve x + y = -1 and 2x + y = 5?
    Donagan
    Top Answerer
    First 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).
  • Question
    How do I plot 1/3 on a graph?
    Donagan
    Top Answerer
    If 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.
  • Question
    Can you just make the equations into linear general form rather than substuite 0?
    Donagan
    Top Answerer
    Yes, you can (assuming the equations are already linear), but substituting zero is a really easy method.
  • Question
    How 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?
    Donagan
    Top Answerer
    It 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.
  • Question
    How do I solve equation using powers?
    Donagan
    Top Answerer
    Graph 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.)
  • Question
    How do I solve x + y = 4, and x - y = 6 graphically?
    Community Answer
    This 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.
  • Question
    Solve the equation graphically x+y=5 and x+y=2.
    Community Answer
    Those 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.
  • Question
    What is x + 18 + 14 = 14?
    I_l1ke_gam3s
    Community Answer
    First 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.
  • Question
    How do I solve y - 2x = -1, and y + x = 5?
    Community Answer
    Either 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.
  • Question
    how do I solve x+y=4, and x-y=2?
    Community Answer
    It'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.
  • Question
    Solve 3x-y=4 and x+2y=6 algebraically.
    Community Answer
    Use 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.
  • Question
    How do I solve the simultaneous equations graphically: 6r+5s=8; 4r+s=3?
    Community Answer
    First 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.
  • Question
    How do I solve y=2x-5, y=x+4?
    Community Answer
    Since the variables are the same, you can set these two equations on opposite sides of an equals sign (2x-5 = x+4). Subtract x on both sides and add 5 to both sides (x=9). Use that value of x and input it into the simpler y=x+4 equation so you get a y value of y=9+4. You'll get y=13.
  • Question
    How do I solve x+y =3, 2x-y =3?
    Community Answer
    Assuming you want to use the graphical method, you would simply graph both equations. Look at the point where the two lines intersect. The x- and y-coordinates of the point of intersection are the x- and y-values you're looking for. (Either the substitution method or the elimination method would probably solve the equations more easily in this particular case.)
  • Question
    How do I solve y-3x=2?
    I_l1ke_gam3s
    Community Answer
    Because there are two unknowns, you need two equations to solve this problem. One equation is not enough. All you can do is solve for a variable in terms of another variable: y = 3x + 2 or x = 2/-3 - y/3.
  • Question
    Solve 2x²+3x+2=0 and -2x²-8x-5=3?
    Donagan
    Top Answerer
    Solve 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.
  • Question
    Where did you get 18,-8?
    Donagan
    Top Answerer
    That 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.
  • Question
    How to solve y=2x2-3x-5 and 2y=2x+11 if the graph isn't perfect?
    Donagan
    Top Answerer
    If 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.
  • Question
    The 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?
    Donagan
    Top Answerer
    Just 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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