Math CentralQuandaries & Queries


Question from Alicia, a student:

I need help with the following equation please show me the steps to complete so that I will know how to do this my self.
2x-y=2, 5x+y=5 Thanks for the help
Here is what I have so far y=2x-2, y=5x+5

Hi Alicia,

The first equation you have solved for y correctly. For the second equation, 5x + y = 5, to solve for you add -5x to each side to get

5x + y = 5
5x + y - 5x = 5 - 5x
y = 5 - 5x.

Thus you have

y = 2x - 2 and y = 5 - 5x.

Since the right side of each of the equations is equal to the same thing, y, they must be equal. Thus

2x - 2 = 5 - 5x.

Solve this equation for x.

I want to show you another way to solve this problem. You start with

2x - y = 2 and 5x + y = 5

Since the left side of the first equation is equal to 2 and the left side of the second equation is equal to 5, if you add the two left sides you must get 2 + 5 = 7. Thus

2x - y + 5x + y = 2 + 5.

Simplifying this equation gives

7x = 7.

Solve for x.

I hope this helps,

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