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Solve using systems answer in a ordered pair
y = –x + 3
y = 4x – 2

1 Answer

6 votes

Answer:

(1,2)

Explanation:

Pre-Solving

We are given the following system of equations:

y = -x + 3

y = 4x - 2

And we want to solve it, with the answer in an ordered pair.

Solving

Because both systems are equal to y, we can set both of the equations equal to each other, and solve for x in that way.

This is possible due to transitivity, which states that if a=b, and b=c, then a=c.

Hence,

-x + 3 = 4x - 2 (same as y=y)

We can add x to both sides.

3 = 5x - 2

Add 2 to both sides.

5 = 5x

Divide both sides by 5.

1 = x

Now, we can use this value to find y.

Substitute 1 as x in either y = -x + 3 or y = 4x - 2

Taking y = -x + 3 for instance:

y = -1 + 3 = 2

So, we now that x=1, y=2.

As an ordered pair, that is (1,2).

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