Question

Solve the system of equations below. Equation 1: 2X+Y=10 Equation 2: x + y = 2 Enter the value of the y value from your solution (in the case of a fraction or decimal solution, round your answer to the nearest tenth).

Answer 1

y = -6

Explanation:

Pre-Solving

We are given the following system of equations:

2x + y = 10

x + y = 2

We want to find the y value of this system.

To do this, we can use elimination, where we will add the equations together to cancel out one of the variables, then evaluate the value of the non-cleared out variable.

Before we can eliminate, we need to make sure that the coefficients on one of the variables are opposites, e.g. 3 and -3.

Since we want the value of y, we can multiply the bottom equation by -2 in order to clear out x.

The bottom equation will therefore be:

-2x - 2y = -4.

Solving

We can rewrite the equations:

2x + y = 10

-2x - 2y = -4

Add them together.

-y = 6

Divide both sides by -1.

y = -6