Question

X+3y=-2
3x+4y=-6
USE SYSTEMS BY SUBSTITUTION.

X=
Y=

Answer 1

X=-2

Y=0

Explanation:

X+y=-2 = x=-2-y

3x+4y=-6

3(-2-y)+4y=-6

-6-3y+4y=-6

y=0

x+3(0)=-2

x=-2

Answer 2

`\boxed {\boxed {\sf (-2,0)}}`

Explanation:

To solve by substitution we must first isolate 1 variable in an equation.

Let's use the first equation.

`x+3y= -2`

Subtract 3y from both sides to isolate the variable x.

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

`x= -2 -3y`

Now we can substitute the expression (-2-3y) in for x in the second equation.

`3x+4y= -6`

`3(-2-3y)+4y= -6`

Distribute the 3. Multiply each term inside the parentheses by 3.

`(3*-2)+ (3*-3y)+4y=-6\\-6-9y+4y=-6`

Combine the like terms on the left side.

`-6-5y= -6`

Add 6 to both sides to isolate the variable.

`-6+6-5y=-6+6\\-5y=0`

Divide both sides by -5.

`-5y/-5=0/-5 \\y=0`

Now we know that y is equal to 0 and can substitute it into the first equation and find x.

`x+3(0)=-2`

`x+0=-2 \\x= -2`

x is equal to -2 and y is equal to 0.