Question

Need help please, solve the system of equations. Check photo

Answer 1

The solution is

`x=(9)/(11)`

`y=(17)/(11)`

Explanation:

We have the system:

-4x+6y=6

-7x+5y=2

I would like to solve this by elimination because I don't feel like rearranging both equations and they both have the same form which is crucial in elimination. The only thing is I will need opposites in a column (where the variable are).

So I'm going to focus on the x's. I want the x part to be opposites.

I know if I multiply the first equation by 7 I will get -28x plus... and if I multiply the last equation by -4 I will get 28x plus... .

28x and -28 are opposites and we all know what happens to opposites when you add them. They zero out; cancel out. That is -28x+28x=0.

So let's multiply first equation by 7 and

multiply bottom equation by -4:

-28x+42y=42

28x-20y=-8

----------------------We are ready to add the equations:

0+22y=34

22y=34

Divide both sides by 22:

y=34/22

Reduce the fraction:

y=17/11 (I divided top and bottom by 2.)

Now if y=17/11 and -4x+6y=6, we can find x by inserting 17/11 for y in the second equation I wrote in this sentence.

`-4x+6\cdot (17)/(11)=6`

Perform the simplification/multiplication of 6 and 17/11:

`-4x+(102)/(11)=6`

Subtact 102/11 on both sides:

`-4x=6-(102)/(11)`

Find a common denominator:

`-4x=(66)/(11)-(102)/(11)`

`-4x=(-102+66)/(11)`

`-4x=(-36)/(11)`

Divide both sides by -4:

`x=(-36)/(-4(11))`

Reduce 36/4 to 9:

`x=(9)/(11)`

`x=(9)/(11)`

The solution is

`x=(9)/(11)`

`y=(17)/(11)`