Solve using the substitution method. Sh 3x + 24y = 24, 27x – 15y = -15 .
3x + 24y = 24
27x - 15y = -15
Divide both sides of the first equation by 3.
x + 8y = 8
Transpose 8y.
x = 8 - 8y
Substitute 8-8y for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.
To solve this 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 for x:
3x + 24y = 24
Subtract 24y from both sides:
3x = 24 - 24y
Divide both sides by 3:
x = 8 - 8y
So, we have x = 8 - 8y as Equation 1.
Step 2: Substitute the expression for x from Equation 1 into the other equation. Let's substitute x = 8 - 8y into the second equation:
27x - 15y = -15
Replace x with 8 - 8y:
27(8 - 8y) - 15y = -15
Simplify the expression:
216 - 216y - 15y = -15
Combine like terms:
-231y = -231
Divide both sides by -231:
y = 1
So, we have y = 1 as the value of y.
Step 3: Substitute the value of y back into Equation 1 to find the value of x:
x = 8 - 8(1)
x = 8 - 8
x = 0
Therefore, the solution to the system of equations is x = 0 and y = 1.