Question

Solve the following system of equations using the substitution method.

y = -5x - 17
-3x - 3y = 3
O A) (-4,-3)
B) (-4,3)
C) (4,3)
D) (4,-3)

Answer 1

`\boxed {\boxed {\sf (B. \ -4, 3)}}`

Explanation:

We are given 2 equations and asked to solve the system of equations using the substitution method.

The 2 equations are:

`y= -5x-17 \\-3x-3y= 3`

The first equation is already solved for y, so we can substitute -5x-17 (the expression that y is equal to) into the second equation.

`-3x-3(-5x-17)=3`

Solve for x by isolating the variable. First, distribute the -3. Multiply each term in parentheses by -3.

`-3x + [ (-3*-5x ) \ + \ (-3* -17)]`

`-3x + [15x + 51]= 3`

`-3x+15x+51=3`

Combine like terms. -3x and 15x can be added because both terms contain the variable x.

`12x+51=3`

51 is being added to 12x. The inverse operation of addition is subtraction. Subtract 51 from both sides of the equation.

`12x+51-51=3-51`

`12x= -48`

x is being multiplied by 12. The inverse operation of multiplication is division. Divide both sides by 12.

`\frac {12x}{12}= (-48)/(12)`

`x= -4`

Now that we have solved for x, we must find y. We know that x is equal to -4, so we can substitute -4 in for x in the first equation.

`y= -5x-17`

`y= -5(-4)-17`

Multiply.

`y=20-17`

Subtract.

`y=3`

Coordinate points are written as (x, y), so the solution to this system of equations is (-4, 3)