Question

use substitution method to solve system
{5x-5y=-45}
{2x+3y=7}

Answer 1

To solve the system of equations using the substitution method, we first solve one equation for one variable and then substitute that expression into the other equation.

Let's solve the first equation for x:

5x - 5y = -45
5x = 5y - 45
x = (5y - 45)/5
x = y - 9

Now, we substitute this expression for x in the second equation:

2x + 3y = 7
2(y - 9) + 3y = 7
2y - 18 + 3y = 7
5y - 18 = 7
5y = 7 + 18
5y = 25
y = 25/5
y = 5

Now, substitute the value of y in the expression for x:

x = y - 9
x = 5 - 9
x = -4

Therefore, the solution to the system of equations is x = -4 and y = 5.