Question

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

Answer 1

Answer:

y = -4, x = 3

Step-by-step 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

$\frac{-x}{-1} =-\frac{7}{-1} -\frac{y}{-1}$

$\frac{-x}{-1}$

Apply the fraction rule: $\frac{-a}{-b} =\frac{a}{b}$

$=\frac{x}{1}$

Apply rule: $\frac{a}{1} =a$

$=x$

Simplify $-\frac{7}{-1} -\frac{y}{-1}$

$-\frac{7}{-1} -\frac{y}{-1}$

Apply rule: $\frac{a}{c} ±\frac{b}{c} =\frac{a±b}{c}$

$=-\frac{7}{-1} -\frac{y}{-1}$

Apply the fraction rule: $\frac{a}{-b} =-\frac{a}{b}$

$=\frac{-7-y}{1}$

Apply rule: $\frac{a}{1} =a$

$=-(-y-7)$

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

$\frac{-4y}{-4} =\frac{16}{-4}$

Simplify $\frac{-4y}{-4} =\frac{16}{-4}$

Simplify $\frac{-4y}{-4}$

Apply the fraction rule: $\frac{-a}{-b}=-\frac{a}{b}$

$=-\frac{16}{4}$

Divide the numbers: $\frac{16}{4} =4$

= - 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

Step-by-step 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