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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.
