Answer:
[tex]\boxed {\boxed {\sf (B. \ -4, 3)}}[/tex]
Step-by-step explanation:
We are given 2 equations and asked to solve the system of equations using the substitution method.
The 2 equations are:
[tex]y= -5x-17 \\-3x-3y= 3[/tex]
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.
[tex]-3x-3(-5x-17)=3[/tex]
Solve for x by isolating the variable. First, distribute the -3. Multiply each term in parentheses by -3.
[tex]-3x + [ (-3*-5x ) \ + \ (-3* -17)][/tex]
[tex]-3x + [15x + 51]= 3[/tex]
[tex]-3x+15x+51=3[/tex]
Combine like terms. -3x and 15x can be added because both terms contain the variable x.
[tex]12x+51=3[/tex]
51 is being added to 12x. The inverse operation of addition is subtraction. Subtract 51 from both sides of the equation.
[tex]12x+51-51=3-51[/tex]
[tex]12x= -48[/tex]
x is being multiplied by 12. The inverse operation of multiplication is division. Divide both sides by 12.
[tex]\frac {12x}{12}= \frac{-48}{12}[/tex]
[tex]x= -4[/tex]
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.
[tex]y= -5x-17[/tex]
[tex]y= -5(-4)-17[/tex]
Multiply.
[tex]y=20-17[/tex]
Subtract.
[tex]y=3[/tex]
Coordinate points are written as (x, y), so the solution to this system of equations is (-4, 3)
