Question

Consider the following pair of equations: y = x + 4 y = −2x − 2.

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Answer 1

To solve the equations y = x + 4 and y = −2x − 2 by substitution, set them equal to each other, solve for x, then substitute x back into one of the equations to find y. The solution is the ordered pair (− 2, 2), where the two lines intersect.

Step-by-step explanation:

Solving Linear Equations by Substitution

To solve the pair of linear equations y = x + 4 and y = −2x − 2 by substitution, you need to follow these steps:

1. Identify the equation that is easiest to solve for one of the variables. In this case, both equations are already solved for y, making substitution straightforward.
2. Since both equations are equal to y, set them equal to each other: x + 4 = −2x − 2.
3. Solve the resulting equation for x: Add 2x to both sides to get 3x + 4 = − 2, and then subtract 4 from both sides to get 3x = − 6. Divide by 3 to find x = − 2.
4. Substitute x back into one of the original equations to solve for y. Using y = x + 4 and substituting − 2 for x, we find y = (− 2) + 4 = 2.
5. Write the solution in ordered pair form: The solution is (− 2, 2).

The ordered pair (− 2, 2) is the point where the two lines represented by the equations intersect, and thus, the solution to the system.