Question

3x-5y =-22
use substitution to solve the system of equations

Answer 1

To solve this system of equations using substitution, we first need to isolate one of the variables in one of the equations. Let's isolate y in the first equation:

3x - 5y = -22
-5y = -3x - 22
y = 3/5x + 22/5

Now we can substitute this expression for y into the second equation:

2x + 3(3/5x + 22/5) = 13

2x + 9/5x + 66/5 = 13
(10/5)x + (9/5)x = 13 - 66/5
(19/5)x = 65/5
x = (65/5) / (19/5)
x = 13 / 19

Now that we have found the value of x, we can substitute it back into the equation we found for y:

y = 3/5(13/19) + 22/5
y = 39/95 + 22/5
y = (39 + 418) / 95
y = 457 / 95

So the solution to the system of equations is x = 13/19 and y = 457/95.