solve using the substitution method.
-8x + y = 18
9x + 13y = 8
-8x + y = 18
9x + 13y = 8
y = 18 + 8x
9x + 13(18 + 8x) = 8
9x + 104x + 234 = 8
113x = -226
x = - 2
Now solve for y.
To solve this system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for a variable in terms of the other variable.
Let's solve the first equation for y:
-8x + y = 18
y = 8x + 18
Step 2: Substitute the expression found in Step 1 into the other equation.
Substitute y = 8x + 18 into the second equation:
9x + 13(8x + 18) = 8
Step 3: Solve the resulting equation for the remaining variable.
Expand and simplify the equation:
9x + 104x + 234 = 8
113x + 234 = 8
113x = -226
x = -2
Step 4: Substitute the value of x back into one of the original equations to find the value of the other variable.
Let's substitute x = -2 into the first equation:
-8(-2) + y = 18
16 + y = 18
y = 2
So, the solution to the system of equations is x = -2 and y = 2.