Question

Use substitution to solve the system.
x-3y=-13
5x-3y=-5

Answer 1

To use substitution, solve one of the equations for one variable and substitute that expression into the other equation.

From the first equation, we can solve for x:

x = 3y - 13

Now substitute this expression for x in the second equation:

5(3y - 13) - 3y = -5

Distribute the 5:

15y - 65 - 3y = -5

Combine like terms:

12y - 65 = -5

Add 65 to both sides:

12y = 60

Divide both sides by 12:

y = 5

Now substitute this value for y back into the expression for x we found earlier:

x = 3(5) - 13

Simplify:

x = 15 - 13

x = 2

Therefore, the solution to the system of equations is x = 2, y = 5.