Solve using the substitution method.
-8x + y = 18
9x + 13y = 8
Add 8x to both sides of first equation.
y = 18 + 8x
9x + 13y = 8
Substitute 18+8x for y in the second equation and solve for x. Insert that value into the first equation to solve for y. Check by putting both values into the second equation.
To solve the given system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation, -8x + y = 18, for y:
Add 8x to both sides: y = 8x + 18.
Step 2: Substitute the expression for the solved variable from step 1 into the other equation.
Substitute the expression (8x + 18) for y in the second equation, 9x + 13y = 8:
9x + 13(8x + 18) = 8.
Step 3: Solve the equation obtained in step 2 for the remaining variable.
Expand within the parentheses:
9x + 104x + 234 = 8.
Combine like terms:
113x + 234 = 8.
Subtract 234 from both sides:
113x = -226.
Divide both sides by 113:
x = -2.
Step 4: Substitute the value of x obtained in step 3 into either of the original equations to solve for the other variable.
Let's substitute x = -2 into the first equation, -8x + y = 18:
-8(-2) + y = 18
16 + y = 18.
Subtract 16 from both sides:
y = 2.
Step 5: Verify the solution by substituting the values of x and y back into both original equations.
Let's check both equations using x = -2 and y = 2:
For the first equation: -8x + y = 18
-8(-2) + 2 = 18
16 + 2 = 18
18 = 18 (true)
For the second equation: 9x + 13y = 8
9(-2) + 13(2) = 8
-18 + 26 = 8
8 = 8 (true)
The solution to the given system of equations is x = -2, y = 2.