Question

Solve by using elimination. Express your answer as an ordered pair.

Answer 1

Greetings.

The answer is (5,4)

Explanation:

Solving by elimination can be done by adding or subtracting of first and two equation.

Find any terms that make themselves = 0.

And that is the y-term.

Our 2y and -2y. If we add each others, we'd get 0 for y-term.

Therefore, we eliminate the y-term first.

$\left \{ {{-x+2y=3} \atop {3x-2y=7}} \right. \\2x=10$

If you are wondering how I get 2x = 10 then here's the explanation.

So we simply add/subtract both equations.

We do -x + 3x = 2x

Then +2y - 2y = 0

And 3 + 7 = 10

That's how we get 2x = 10.

Basically Add/Subtract in Vertical way.

$2x=10\\x=5$

We may get the x-value but we need to know the y-value too.

Therefore, substitute x = 5 into any given equations. I suggest you to substitute the x-value in any equations with less coefficient value.

I'd rather substitute x = 5 in -x+2y = 3.

$-x+2y=3$

Substitute x = 5 in -x + 2y = 3

$-5+2y=3\\2y=3+5\\2y=8\\y=\frac{8}{2}\\y=4$

Therefore, when x = 5, y = 4. Since you want the answer in ordered pairs then It's (5,4).