y=3x-2

y=8-2x

what type of system is this?

y=3x-2

y=8-2x

what type of system is this?

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This is a system of linear equations in two variables. We have several ways to solve it:

1. By graphing, either manually on graph paper, or with a graphing calculator.

2. By substitition, which is the best way to solve this one (see below).

3. By linear combination, which involves rewriting each to the form Ax + By = C, writing them with one above the other, and then multiplying one or both by appropriate numbers so that when the two equations are added together, one of the variables disappears. You then solve for the remaining variable, and substitute to find the other one.

The easiest method for this problem is substitution, since you alread have two "y = " equations. Simply set them equal to each other (a substitution that will eliminate the y variable temporarily):

3x - 2 = 8 - 2x

Now add 2x to each side, and then add 2 to each side, leaving x's on the left and numbers on the right:

3x - 2 = 8 - 2x

+2x +2x

________________________

5x - 2 = 8

+2 +2

____________________

5x = 10

**x = 2**

Now to find y, substitue x = 2 into one of the original equations. We'll use the first one:

y = 3(2) - 4

= 6 - 4

**y = 4**

Yoiur solution set is **(2,4)**