Question

Use elimination to solve the system. 2x +5y =24 4x +3y =20

Answer 1

x=2 and y=4

Explanation:

1. first you have to order both equations like this:

2x +5y =24

4x +3y =20

2. second you can multiply all the first equation by -2

-2(2x +5y =24)

4x +3y =20

***and you can get this*** (becareful with the signs)

-4x-10y=-48

4x +3y =20

well the next step that you are going to do is combine both equation *becareful with the signs*

and then you can eliminate x and you are going to left with this

-7y= - 28

after this you have to divide - 7 in both sides to solve for y

-7y= - 28

-7 -7

y=4

so now you know the value of y to solve for x do we need to use one of the original equations and solve for x

2x +5y =24 this is one of the original equations.

2x +5(4) =24. we change the y or y's for 4

2x+20 = 24 we multiply 5×4 to get 20

-20 -20 we substract the 20 in both sides

2x=4

2 2 and finally we divide 2 in both sides

x=2 and we get this.

in this part I'm going to solve for x using the other equation and you can see we get the same answer (in your work is not necessary write this part⬇️)***here are the same steps as the last one but just that I don't going to write the explanation to don't continuing making this too long***

4x +3y =20

4x+3(4)=20

4x+12=20

-12 -12

4x=8

4 4

x=2

I hope and this helps and I'm really sorry for make this very long.

Answer 2

x=2, y=4

Explanation:

In order to use elimination, we need to make one of the 2 variables x and y equal to each other in both equations. To do that, we need to multiply an equation. I'm going to eliminate x.

So, to do this, I multiply the first equation by 2-

2(2x+5y) = 2(24)

4x+10y= 48.

Now, I subtract both equations.

4x+10y= 48

- 4x+3y= 20

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

7y= 28

y=4.

Now substitute y=4 into an equation. I'm gonna take the first one.

2x + 5y= 24

2x + 5(4)= 24

2x+20=24

2x=4

x=2.

Hope this helps!