Question

PleaseeeeeHelp!!!!!!!!!!!!

Answer 1

x = -2, y = -5

Explanation:

Isolate x for 3x - 2y = 4

3x - 2y = 4

Add 2y to both sides

3x -2y + 2y = 4 + 2y

Simplify

3x = 4 + 2y

Divide both sides by 3

`(3x)/(3) =(4)/(3) +(2y)/(3)`

Simplify

`x=(4+2y)/(3)`

Now we substitute
`x=(4+2y)/(3)` for x in 4x - 3y = 7

`4*(4+2y)/(3)-3y=7`

Isolate y for
`4*(4+2y)/(3)-3y=7`

`4*(4+2y)/(3)-3y=7`

Expand
`4*(4+2y)/(3)-3y`

`4*(4+2y)/(3) =(16+8y)/(3)`

`4*(4+2y)/(3)`

Multiply fractions:
`a*(b)/(c) =(a*b)/(c)`

`=((4+2y)*4)/(3)`

Expand
`(4+2y)*4`

`=4(4+2y)`

Apply the distributive law:
`a(b+c)=ab+ac`

`a=4, b=4,c=2y`

`=4*4+4*2y`

Simplify
`4*4+4*2y`

Multiply the numbers:
`4*4 = 16`

`=16+4*2y`

Multiply the numbers:
`4*2=8`

`=16+8y`

`=(16+8y)/(3)`

`=(8y+16)/(3)-3y`

Convert element to fraction:
`3y=(3y3)/(3)`

`=(16+8y)/(3) -(3y*3)/(3)`

Since the denominators are equal, combine the fractions:
`(a)/(c)`±
`(b)/(c)= (a±b)/(c)`

`=(16+8y-3y*3)/(3)`

`16+8y-3y*3`

Multiply the numbers:
`3*3=9`

`=16+8y-9y`

Add similar elements:
`8y-9y=-y`

`=16-y`

`=(16-y)/(3)`

Apply the fraction rule:
`(a)/(c)`±
`(b)/(c)= (a±b)/(c)`

`(16-y)/(3) =(16)/(3) -(y)/(3)`

`=(16)/(3)-(y)/(3)`

`(16)/(3) -(y)/(3) =7`

Multiply both sides by 3

`(16)/(3)*3-(y)/(3) *3=7*3`

Simplify

`16-y=21`

Subtract 16 from both sides

`16-y-16=21-16`

Simplify

`-y=5`

Divide both sides by -1

`(-y)/(-1) =(5)/(-1)`

Simplify

`y=-5`

For
`x=(4+2y)/(3)` substitute
`y=-5`

`x=(4+2y(-5))/(3)`

Remove parentheses:
`(-a)=-a`

`=(4+2y*5)/(3)`

Multiply the numbers:
`2*5=10`

`=4-10`

Subtract the numbers:
`4-10=-6`

`=-6`

`=(-6)/(3)`

Apply the fraction rule:
`(-a)/(b) =-(a)/(b)`

`=-(6)/(3)`

Divide the numbers:
`(6)/(3)=2`

`=-2`

The solutions to the system of equations are

`y=-5,x=-2`

Checking answers

Plug in
`x=-2` and
`y=-5` into
`3x-2y=4` and
`4x-3y=7`

`3(-2)-2(-5)=4`

Remove parentheses:
`(-a)=-a,-(-a)=a`

`=3*2+2=5`

Multiply the numbers:
`3*2=6`

`=-6+2*5`

Multiply the numbers:
`2*5=10`

`=-6+10`

Add/subtract the numbers:
`-6+10=4`

`=4`

First equation proven true

Substitute the values of x and y into the second equation

`4(-2)-3(-5)=7`

Follow the PEMDAS order of operations

Multiply and divide left to right
`4(-2)`

`4(-2)`

Apply rule
`a*(-b)=-a*b`

`4(-2)=-4*2=-8`

`=-8`

`=-8-3(-5)`

Multiply and divide left to right
`3(-5)`

`3(-5)`

Apply rule
`a*(-b)=-a*b`

`3*(-5)=-3*5=-15`

`=-15`

`=-8-(-15)`

Add and subtract left to right
`-8-(-15)`

`-8-(-15)`

Apply rule
`-(-a)=+a`

`-(-15)=+15`

`=-8+15`

`-8+15=7`

`=7`

Second equation proven true.

Both equations are true with
`x=-2` and
`y=-5`