solve for x using the substitution method -8x + y = 18, 9x + 13y = 8
first equation:
y= 18+8x
put that into
9x+13(18+8x)=8
and solve for x.
To solve the system of equations using the substitution method, we need to solve one equation for one variable, and then substitute that expression into the other equation.
Let's solve the first equation for y:
-8x + y = 18
To isolate y, we can add 8x to both sides:
y = 8x + 18
Now, substitute this expression for y into the second equation:
9x + 13(8x + 18) = 8
Distribute the 13 to the terms inside the parentheses:
9x + 104x + 234 = 8
Combine like terms:
113x + 234 = 8
Next, isolate x by subtracting 234 from both sides:
113x = 8 - 234
Simplify:
113x = -226
Now, divide both sides by 113 to solve for x:
x = -226/113
Simplify:
x = -2
Now that we have the value of x, we can substitute it back into the first equation to find y:
-8(-2) + y = 18
Simplify:
16 + y = 18
Subtract 16 from both sides:
y = 18 - 16
Simplify:
y = 2
Therefore, the solution to the system of equations is x = -2 and y = 2.