Question

How can I solve this following system of equation by substitution 3x-7y=4 and 2x+y=-3

Answer 1

To solve the system of equations, we first need to isolate one of the variables in one of the equations. For this example, I'll isolate x from the second equation, because it will be much easier and I'll end up with simpler fractions.

2x + y = -3   Given
2x = -y - 3   Subtract y from both sides
x = -1/2y - 3/2

Now, we need to substitute x in the other equation for -1/2y - 3/2 so that we can find y.

3(-1/2y - 3/2) - 7y = 4   Substitute
-3/2y - 9/2 - 7y = 4   Multiply
-17/2y - 9/2 = 4   Collect like terms (wow, this is turning out to be a tough one, isn't it?)
-17/2y = 17/2
y = -1

Wow, such complicated work for such a simple answer. Anyway, now we can plug that into our answer for x to get x's value.

x = -1/2y - 3/2   Given
x = -1/2(-1) - 3/2   Substitute
x = 1/2 - 3/2   Multiply
x = -1   Subtract

Therefore, the solution for the system of equations is (-1,-1). It can be a bit intimidating with all the fractions, but the question decided to be nice and give us simple answers.

Hope this helps!