Question

-x + y=-7
-3x - y = -5

Answer 1

y = -4, x = 3

Explanation:

-x + y = -7

-3x - y = -5

Isolate x for -x + y = -7.

-x + y = -7

Subtract y from both sides.

-x + y - y = -7 - y

Simplify.

-x = -7 - y

Divide both sides by -1

`(-x)/(-1) =-(7)/(-1) -(y)/(-1)`

`(-x)/(-1)`

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

`=(x)/(1)`

Apply rule:
`(a)/(1) =a`

`=x`

Simplify
`-(7)/(-1) -(y)/(-1)`

`-(7)/(-1) -(y)/(-1)`

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

`=-(7)/(-1) -(y)/(-1)`

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

`=(-7-y)/(1)`

Apply rule:
`(a)/(1) =a`

`=-(-y-7)`

Distribute parentheses.

`=-(-7)-(-y)`

Apply minus - plus rule.

`-(-a)=a`

`=7+y`

`x=7+y`

Substitute
`x=7+y`

`[-3(7+y)-y=-5]`

Isolate y for
`-3(7+y)-y=-5`

`-3(7+y)-y=-5`

Expand -3 (7 + y )

-3 (7 + y )

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

`a=-3,b=7, c=y`

`=-3*7+(-3)y`

Apply minus - plus rule

`+(-a)=-a`

`=-3*7-3y`

Multiply the numbers: 3 * 7 = 21

`=-21-3y`

`-21-3y-y=-5`

Add similar elements:
`-3-y=-4y`

`-21-4y=-5`

Add 21 to both sides.

`-21-4y+21=-5+21`

Simplify.

`-4y=16`\

Divide both sides by -4

`(-4y)/(-4) =(16)/(-4)`

Simplify
`(-4y)/(-4) =(16)/(-4)`

Simplify
`(-4y)/(-4)`

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

`=-(16)/(4)`

Divide the numbers:
`(16)/(4) =4`

= - 4

y = -4

For x = 7 + y, substitute y = -4

x = 7 - 4

Subtract the numbers: 7 - 4 = 3

= 3

x = 3

y = -4, x = 3

`(3,-4)`

Answer 2

Answer: x= - 3; y = -4

Explanation:

-x + y = -7

-3x - y = -5

-4x = -12

x= -12 /- 4

x= - 3

-x + y = -7

-(-3) + y = - 7

3 + y = - 7

y = - 7 + 3

y = -4

-x + y = -7

-3 - 4 = - 7

- 7 = - 7