Question

-5x+3y=-8 3x−7y=-3 solve for y and x.

Answer 1

To solve this system of equations, we can use either the substitution method or the elimination method.

Let's use the substitution method:

1. Solve the first equation for x:
-5x + 3y = -8
-5x = -3y - 8
x = (3y + 8) / 5

2. Substitute this expression for x into the second equation:
3((3y + 8) / 5) - 7y = -3
(9y + 24) / 5 - 7y = -3
9y + 24 - 35y = -15
-26y + 24 = -15
-26y = -39
y = 39 / 26
y = 3 / 2

3. Substitute the value of y back into the equation to solve for x:
x = (3(3/2) + 8) / 5
x = (9/2 + 8) / 5
x = (9/2 + 16/2) / 5
x = 25 / 2 / 5
x = 25 / 10
x = 5 / 2

Therefore, the solution to the system of equations is:
x = 5 / 2
y = 3 / 2