Question

SOMEONE HELP ME PLEASE MY LAST DAY TO TURN THIS IN!

Solving Systems of Equations by Elimination
1) 5x + 2y= 21
-x - y= -9
2) 3x + 2y= -13
3x+4y= 1
3) 7x + 3y= 22
4y= 20
4) -2x + y= 10
4x - y= -14

Answer 1

Hello!

I'll solve the first two systems.

1)

`\left \{ {{5x+2y=21} \atop {-x-y=-9}} \right.`

Multiply the second equation in the system by 2 to be able to cancel out y-terms:


`-x-y=-9`

`2(-x-y=-9)`

`-2x-2y=-18`

Now, add the equations together:


`\left \ {{5x+2y=21} \atop {-2x-2y=-18}} \right.`
_____________

`3x-0=3`

`3x=3`

`x=1`

Plug 1 for x into one of the original equations to find y:


`5x+2y=21`

`5(1)+2y=21`

`5+2y = 21`

`2y=16`

`y =8`

Check work by plugging your values for x and y back into both original equations:


`\left \ {{5x+2y=21} \atop {-x-y=-9}} \right.`


`\left \ {{5(1)+2(8)=21} \atop {-(1)-(8)=-9}} \right.`


`\left \ {{5+16=21} \atop {-1-8=-9}} \right.`

Both are true; x = 1 and y = 8.

2)

`\left \ {{3x+2y=13} \atop {3x+4y=1}} \right.`

For this system, to be able to cancel out x-terms, you can multiply either equation by -1; I'll use the bottom equation:


`-1(3x+4y=1)`

`-3x-4y=-1`

Now add the equations together:


`\left \ {{3x+2y=-13} \atop {-3x-4y=-1}} \right.`
_____________

`0-2y=-14`

`-2y = -14`

`y=7`

Plug 7 for y into either of the original equation to solve for x:


`3x+2(7)=-13`

`3x+14=-13`

`3x = -27`

`x=-9`

Plug -9 for x and 7 for y into each original equation to check work:


`\left \ {{3(-9)+2(7)=-13} \atop {3(-9)+4(7)=1}} \right.`


`\left \ {{-27+14=-13} \atop {-27+28=1}} \right.`

Both are correct; x = -9 and y = 7.

Apply these steps to the last two systems and you're good to go. (: