Q&A for How to Solve Systems of Algebraic Equations Containing Two Variables

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If the first step is, R - R/2 =6, what is the second step?

Donagan

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The second step is to change R to 2R/2. (It's easier to subtract R/2 from 2R/2.) Realize that "R/2" means "one-half of an R." So "R - R/2" means "subtract half-an-R from a full R," which leaves you with half-an-R. So the equation really means that half-an-R equals 6. That means that a full R equals 12.

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What is the easiest way to do this type of algebra?

Donagan

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The substitution method often involves the least amount of work, but the elimination method is sometimes easier. It just depends on the equations involved.

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A house and its furniture were bought for Rs. 5000. The house was sold at a gain of 10% and the furniture at a loss of 5%. A profit of 4% was made on the total outlay. How do I find the original cost?

Donagan

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The original cost was defined as Rs. 5,000.

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What if there is only an expression and no answer?

Donagan

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Assuming you mean that no equation has been given, the expression cannot be "solved."

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How would I solve an equation if it has 2 variables on one side and 1 on the other?

Donagan

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If you mean that there's one equation containing two variables, one of them appearing on both sides of the equation and the other appearing on only one side, move one of the variables by adding, subtracting, multiplying or dividing until one of the variables is on one side of the equation, and the other variable is on the other side. Then isolate either of the variables so that it stands alone without a coefficient or other accompanying numbers. You have now solved the equation for the isolated variable. You can do the same thing for the other variable, too, if you want. As for an equation in three variables, isolate one of the variables, and evaluate it in terms of the other two.

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How do I solve 10 = (10 - x) + (21 - 2y)?

Donagan

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This equation has two unknowns. Therefore neither unknown can be evaluated except in terms of the other. So simplify the right side. Then solve for x in terms of y and/or for y in terms of x.

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What do I need to do if I have to fill out a table of values where both x and y are blank?

Donagan

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Presumably you have an equation in x and y. Choose conveniently low (positive and/or negative) values for the independent variable (x or y). Then calculate the corresponding values for the dependent variable. Place these values in the appropriate columns of the table.

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h = (d+14.37) x tan20 - how do i find h?

Community Answer

The tangent of 20° is 0.364. h = (d + 14.37)(0.364) = 0.364d + 5.23. (Without knowing the value of d, this is as far as you can go.)

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Solve 2x + 18 = 20 and find the value of 3x.

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2x + 18 = 20. So 2x = 20 - 18 = 2, and x = 1. Then 3x = (3)(1) = 3.

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5x + 3y = 12, -5x + 6y = 10.

I_l1ke_gam3s

Community Answer

Adding these two equations together, we get 9y = 22, so y = 22/9. Then 5x + 3(22/9) = 12. 5x + 66/9 = 12. 5x = 12 - 66/9 = 108/9 - 66/9 = 39/9. Divide both sides by 5, so that x = 39/45 = 13/15.

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How do you solve this: a + b = 0, and 2a - b = 1?

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Use the elimination method. Add the two equations together: 3a = 1. So a = 1/3. Plug that a-value into either original equation: (1/3) + b = 0. So b = -1/3.

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How can you solve for two unknowns using three equations?

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Assuming you mean that all three equations contain both unknowns, you could ignore one of the equations, because all you need is two. Use the usual steps in solving for two unknowns using two simultaneous equations. See Solve Systems of Algebraic Equations Containing Two Variables .

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