Question

Can someone plz help me with this!

Answer 1

(arranged from top to bottom)

System #3, where x=6

System #1, where x=4

System #7, where x=3

System #5, where x=2

System #2, where x=1

Explanation:

System #1: x=4

`2x+y=10\\x-3y=-2`

To solve, start by isolating your first equation for y.

`2x+y=10\\y=-2x+10`

Now, plug this value of y into your second equation.

`x-3(-2x+10)=-2\\x+6x-30=-2\\7x=28\\x=4`

System #2: x=1

`x+2y=5\\2x+y=4`

Isolate your second equation for y.

`2x+y=4\\y=-2x+4`

Plug this value of y into your first equation.

`x+2(-2x+4)=5\\x+(-4x)+8=5\\x-4x+8=5\\-3x=-3\\x=1`

System #3: x=6

`5x+y=33\\x=18-4y`

Isolate your first equation for y.

`5x+y=33\\y=-5x+33`

Plug this value of y into your second equation.

`x=18-4(-5x+33)\\x=18+20x-132\\-19x=-114\\x=6`

System #4: all real numbers (not included in your diagram)

`y=13-2x\\8x+4y=52`

Plug your value of y into your second equation.

`8x+4(13-2x)=52\\8x+52-8x=52\\0=0`

all real numbers are solutions

System #5: x=2

`x+3y=5\\6x-y=11`

Isolate your second equation for y.

`6x-y=11\\-y=-6x+11\\y=6x-11`

Plug in your value of y to your first equation.

`x+3(6x-11)=5\\x+18x-33=5\\19x=38\\x=2`

System #6: no solution (not included in your diagram)

`2x+y=10\\-6x-3y=-2`

Isolate your first equation for y.

`2x+y=10\\y=-2x+10`

Plug your value of y into your second equation.

`-6x-3(-2x+10)=-2\\-6x+6x-30=-2\\-30=-2`

no solution

System #7: x=3

`y=10+x\\2x+3y=45`

Plug your value of y into your second equation.

`2x+3(10+x)=45\\2x+30+3x=45\\5x=15\\x=3`