Solve the system using substitution.
6x + y = 12
4x + 6y = −8
A. (2 1/2,3)
B. (−2 1/2,−3)
C. (2 1/2,−3)
D. no solution
I GOT B!
Wrong, the answer is C.
To solve the system using substitution, follow these steps:
1. Solve one equation for one variable in terms of the other variable.
Let's solve the first equation for y:
6x + y = 12
y = 12 - 6x
2. Substitute the expression for the variable from step 1 into the other equation.
Now, substitute 12 - 6x for y in the second equation:
4x + 6(12 - 6x) = -8
3. Simplify and solve for x.
Distribute the 6:
4x + 72 - 36x = -8
Combine like terms:
-32x + 72 = -8
Subtract 72 from both sides:
-32x = -80
Divide by -32:
x = (-80)/(-32)
x = 80/32
x = 2.5
4. Substitute the value of x back into one of the original equations to find the value of y.
Let's use the first equation:
6x + y = 12
6(2.5) + y = 12
15 + y = 12
Subtract 15 from both sides:
y = 12 - 15
y = -3
Therefore, the solution to the system of equations is x = 2.5 and y = -3. So the correct answer is C. (2 1/2, -3).
To solve the system using substitution, we need to solve one equation for one variable and substitute it into the other equation.
Let's solve the first equation, 6x + y = 12, for y:
y = 12 - 6x
Now, substitute this expression for y in the second equation, 4x + 6y = -8:
4x + 6(12 - 6x) = -8
Now, simplify and solve for x:
4x + 72 - 36x = -8
-32x + 72 = -8
-32x = -8 - 72
-32x = -80
x = -80 / -32
x = 2.5
Now substitute this value of x back into the first equation to find y:
6(2.5) + y = 12
15 + y = 12
y = 12 - 15
y = -3
Therefore, the solution to the system of equations is x = 2.5 and y = -3. So, the correct answer is C. (2 1/2, -3). Good job on getting the correct answer!