How do you use the Substitution Method for for 7x-2y equals 6 and 9x-3y equals 6?

Answer 1

Given these two equations:

7x - 2y = 6

9x - 3y = 6

you start my taking either one of them, and solving it for either x or y. Let's start with the first one, and solve for y:

7x - 2y = 6

∴ -2y = 6 - 7x

∴ y = -3 + 7x / 2

Now you can take that definition of y, and substitute it into the other equation:

9x - 3y = 6

∴ 9x - 3(-3 + 7x / 2) = 6

We now have an equation with only one variable, x, and can solve it as follows:

9x - 3(-3 + 7x / 2) = 6

∴3x + 3 - 7x/2 = 2

∴3x - 7x/2 = -1

∴6x/2 - 7x/2 = -1

∴-x/2 = -1

∴x = 2

Finally, you can take that value of x, and plug it into either of the original equations in order to calculate y:

7x - 2y = 6

∴14 - 2y = 6

∴-2y = -8

∴y = 4

You can then confirm that this is correct, by plugging those values into the other equation to see if they hold true:

9x - 3y = 6

∴9(2) - 3(4) = 6

∴18 - 12 = 6

∴6 = 6

And since that holds true, you know your answer is correct. x is equal to 2, and y is equal to 4.

Note that you can start by solving for either x or y, with either of the original equations. It doesn't matter which combination you start with. The key technique here is to solve one of the equations for either x or y, and then take that solution and plug it into the other equation.