Solve by the substitution method. What is the solution of the system?
3x+9y=48
-6x+y=56
To use the substitution method, you solve one equation for x, and then substitute that expression for x in the other equation. or, you can solve for y if it's easier.
3x + 9y = 48
3x = 48 - 97
x = 16 - 3y
-6x + y = 56
-6(16-3y) + y = 56
-96 + 19y = 56
19y = 152
y = 8
so,
x = 16 - 24 = -8
To solve the system of equations by the substitution method, we need to solve one of the equations for one variable and substitute it into the other equation.
Let's solve the second equation for y:
-6x + y = 56
y = 6x + 56
Now, substitute this expression for y in the first equation:
3x + 9(6x + 56) = 48
Distribute the 9:
3x + 54x + 504 = 48
Combine like terms:
57x + 504 = 48
Subtract 504 from both sides:
57x = 48 - 504
57x = -456
Divide both sides by 57 to isolate x:
x = -456 / 57
x = -8
Now that we have the value of x, substitute it back into either of the equations to find the value of y. Let's use the second equation:
-6x + y = 56
-6(-8) + y = 56
48 + y = 56
Subtract 48 from both sides:
y = 56 - 48
y = 8
So, the solution to the system of equations is x = -8 and y = 8.