Question

Use the substitution method to solve the following system of equations:

4x − y = 3
7x − 9y = −2

Answer 1

using the first equation:
4x = y + 3 ---> y = 4x - 3
We then substitute this into the second equation:
7x - 9(4x-3) = -2 ---> 7x - 9x + 27 = -2 ---> -2x = -29 ---> x = 14.5

Answer 2

x=1

y=1

Explanation:

First step, we isolate one variable from one equation. Let's isolate y from the first equation:

`4x-y=3\\-y = 3-4x\\-1*-y=-1*(3+4x)\\y=-3+4x`

Next we substitute the y value in the second equation:

`y=7x-9y = -2\\7x-9*(-3+4x)=-2\\7x+27-36x=-2\\-29x=-29\\x=1`

Now, we replace the x value in the equation where y is isolated:

`y=-3+4x\\y=-3+4*1`

`y=1`