Question

How do you solve y = -x and y = -4x + 12 by substituting with this system of equations and find the value of x and y?

Answer 1

To solve the system of equations y = -x and y = -4x + 12 by substitution set the equations equal, solve for x to get x = 4, and substitute back into either equation to find y, which is -4. The solution is x = 4 and y = -4.

Step-by-step explanation:

To solve the system of equations y = -x and y = -4x + 12 using the method of substitution, first recognize that both equations are already solved for y, which makes substitution straightforward.

We set the two equations equal to each other since they both represent y.

1. -x = -4x + 12
2. Add 4x to both sides of the equation, to isolate terms with x on one side: 3x = 12
3. Divide both sides by 3 to solve for x: x = 4

Now that we have the value of x, we can substitute it back into either of the original equations to find y. Substituting x = 4 into y = -x:

1. y = -(4)
2. y = -4

Thus, the solution to the system of equations is x = 4 and y = -4.