Question

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

Answer 1

Greetings again.

The answer is (-2,5)

Explanation:

What we need to do is to eliminate either x-term or y-term. Eliminating the terms that you don't have to multiply to get the same terms for both equations is better.

For this one, there're no terms that make 0.

And what do we do if there are no terms that can be eliminated?

The answer is, multiply one of the equation by -1. To make another equation have opposite negative and positive side. -3y + 3y = 0.

I'll multiply -1 in the second equation.

$2x+3y=11$

Multiply the whole equation by -1.

$2x(-1)+3y(-1)=11(-1)\\-2x-3y=-11$

Remind that negative multiply positive equal negative.

Now then we replace the old equation with -2x - 3y = -11

$\left \{ {{6x+3y=3} \atop {-2x-3y=-11}} \right.$

Then add/subtract vertically.

6x-2x = 4x

3y - 3y = 0

3 - 11 = -8

Therefore, we get 4x = -8

$4x=-8\\x=-2$

Because this is the system of two linear equations. We need to find the y-term/value too.

Substitute x = -2 in any given equations. choose any equations you'd like to substitute in. For me, I'll substitute in the equation with less coefficient value and that is the second equation.

$2x+3y=11$

Substitute x = -2 in the equation.

$2(-2)+3y=11\\-4+3y=11\\3y=11+4\\3y=15\\y=5$

Thus, when x = -2, y = 5. Since you want the answer as an ordered pairs. The answer is (-2,5)

Answer 2

Answer:

(-2, 5)

Step-by-step explanation:

we subtract 6x+3y=3 by 2x+3y=11 to get 4x=-8.

we divide both sides by 4 to get x. x=-2

We subsitute -2 for the second equation to get:

2(-2)+3y=11

=-4+3y=11

=3y=15

y=5