Question

Solve the following system using substitution. What is the solution to the given system?%0D%0A%0D%0Ay = −4x −1 and 2y + 2 = −12x%0D%0A%0D%0A %0D%0A=%0D%0A %0D%0A−%0D%0A4%0D%0A%0D%0A %0D%0A−%0D%0A1%0D%0A %0D%0A%0D%0A%0D%0A%0D%0A %0D%0A %0D%0A2%0D%0A%0D%0A %0D%0A+%0D%0A %0D%0A2%0D%0A %0D%0A=%0D%0A %0D%0A−%0D%0A12%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(-1, 1)%0D%0A(-1, 1)%0D%0A%0D%0A(0, -1)%0D%0A(0, -1)%0D%0A%0D%0A(-2, 0)%0D%0A(-2, 0)%0D%0A%0D%0A(0, 0)%0D%0A(0, 0)

Answer 1

To solve the given system using substitution, we'll solve one equation for one variable and substitute it into the other equation.

1) We have the equation y = -4x - 1.
2) We'll substitute this expression for y into the second equation:

2(-4x - 1) + 2 = -12x

Now, we'll simplify and solve for x:

-8x - 2 + 2 = -12x
-8x = -12x

Adding 8x to both sides:

0 = -4x

Dividing by -4:

0 = x

Now that we know x = 0, we can substitute this value into the first equation to find y:

y = -4(0) - 1
y = -1

Therefore, the solution to the system is (0, -1).