Question

use elimination method to solve the system of equations. Choose the correct order pair. -x+5y=-4 4x+4y=16

Answer 1

(4,0)

Explanation:

So we have the system:

-x+5y=-4

4x+4y=16

--------------

We are asked to solve this for elimination.

We aren't totally setup for elimination though.

Both equations are in the same form, the form being ax+by=c form, so we are good there.

Now the other requirement is one the columns that contain variables need to be opposites (you will add) or same (you will subtract).

I'm going to multiply the first equation by 4. The reason I'm going to do this is because the first column will contain -4x and 4x. Those are opposites. When you add opposites, you get 0 (they cancel).

So applying the multiplication of 4 to first equation gives:

-4x+20y=-16

4x+ 4y=16

----------------- Add the equations now.

0x+24y=0 Again this is called elimination, because we made it to where a variable is canceled when combining the equations.

0x+24y=0

0+ 24y=0

24y=0

Divide both sides by 24:

y=0

So using one of the equations (you only need one of them) along with the y=0, let's find x.

I'm going to go with -x+5y=-4 with y=0.

Plugging in the 0 for y gives us:

-x+5y =-4

-x+5(0)=-4

-x+ 0 =-4

-x =-4

Multiply both sides by -1:

x =4

The solution is (x,y)=(4,0).

Answer 2

The ordered pair is

(4,0)

EXPLANATION

To solve a simultaneous equation using the elimination method means making the coefficient of one of the variables the same. We then add or subtract to eliminate that variable.

The given system has equations:

`- x + 5y = - 4...(1)`

`4x + 4y = 16...(2)`

Divide the second equation by 4

`x + y = 4...(3)`

Add equation (1) and (3) to eliminate x.

`\implies \: 5y + y = - 4 + 4`

`\implies \: 6y = 0`

`\implies \: y = (0)/(6) = 0`

Put

`y = 0`

into the first equation to get:

`- x + 5 * 0 = - 4`

`- x = - 4`

`\therefore \: x = 4`

The ordered pair is

(4,0)