Solve using the substitution method.
-5x + y = 16
9x + 13y = 60
From the first equation, you see that y = 5x+16
so, plug that into the 2nd equation and solve for y.
Then you can figure out x.
To solve this system of equations using the substitution method, we need to solve one equation for one variable and substitute that into the other equation. Let's solve the first equation for y:
-5x + y = 16
Rearrange the equation to isolate y:
y = 5x + 16
Now, substitute this expression for y into the second equation:
9x + 13(5x + 16) = 60
Distribute the 13 to the terms inside the parentheses:
9x + 65x + 208 = 60
Combine like terms:
74x + 208 = 60
Subtract 208 from both sides:
74x = -148
Divide both sides by 74:
x = -2
Now, substitute the value of x back into the equation we found for y:
y = 5(-2) + 16
y = -10 + 16
y = 6
Therefore, the solution to the system of equations is x = -2 and y = 6.