Solve the system of equations by substitution. y = -4 -x + 3y - 2z = 4 x + 2y + z = -19 ____

Substitute y = -4: Substitute y = -4 into the second equation -x + 3y - 2z = 4. -x + 3(-4) - 2z = 4 -x - 12 - 2z = 4Add 12 to isolate: Add 12 to both sides to isolate terms with variables on one side. -x - 2z = 4 + 12 -x - 2z = 16Substitute y = -4: Now, substitute y = -4 into the third equation x + 2y + z = -19. x + 2(-4) + z = -19 x - 8 + z = -19Add 8 to isolate: Add 8 to both sides to isolate terms with variables on one side. x + z = -19 + 8 x + z = -11Two equations with x and z: Now we have two equations with x and z: 1) -x - 2z = 16 2) x + z = -11 Let's solve for z by adding the two equations together. (-x - 2z) + (x + z) = 16 - 11 -x + x - 2z + z = 5 -z = 5Divide both sides: Divide both sides by -1 to solve for z. z = -5Substitute z = -5: Substitute z = -5 back into the equation x + z = -11 to find x. x + (-5) = -11 x - 5 = -11Add 5 to solve: Add 5 to both sides to solve for x. x = -11 + 5 x = -6Solution is (-6, -4, -5): We have found the values for x and z, and we were given y = -4. So the solution is (x, y, z) = (-6, -4, -5).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system of equations by substitution. $\newline$ $y = -4$ $\newline$ $-x + 3y - 2z = 4$ $\newline$ $x + 2y + z = -19$

View step-by-step help

Home

Math Problems

Algebra 2

Solve a system of equations in three variables using substitution

Full solution

Q. Solve the system of equations by substitution.

\newline

y = -4

\newline

-x + 3y - 2z = 4

\newline

x + 2y + z = -19

Substitute $y = -4$ : Substitute $y = -4$ into the second equation $-x + 3y - 2z = 4$ .
$-x + 3(-4) - 2z = 4$
$-x - 12 - 2z = 4$
Add $12$ to isolate: Add $12$ to both sides to isolate terms with variables on one side. $\newline$ $-x - 2z = 4 + 12$ $\newline$ $-x - 2z = 16$
Substitute $y = -4$ : Now, substitute $y = -4$ into the third equation $x + 2y + z = -19$ . $\newline$ $x + 2(-4) + z = -19$ $\newline$ $x - 8 + z = -19$
Add $8$ to isolate: Add $8$ to both sides to isolate terms with variables on one side. $\newline$ $x + z = -19 + 8$ $\newline$ $x + z = -11$
Two equations with x and z: Now we have two equations with x and z: $\newline$ $1$ ) $-x - 2z = 16$ $\newline$ $2$ ) $x + z = -11$ $\newline$ Let's solve for z by adding the two equations together. $\newline$ $(-x - 2z) + (x + z) = 16 - 11$ $\newline$ $-x + x - 2z + z = 5$ $\newline$ $-z = 5$
Divide both sides: Divide both sides by $-1$ to solve for $z$ . $z = -5$
Substitute $z = -5$ : Substitute $z = -5$ back into the equation $x + z = -11$ to find $x$ .
$x + (-5) = -11$
$x - 5 = -11$
Add $5$ to solve: Add $5$ to both sides to solve for $x$ . $x = -11 + 5$ $x = -6$
Solution is $(-6, -4, -5)$ : We have found the values for $x$ and $z$ , and we were given $y = -4$ . $\newline$ So the solution is $(x, y, z) = (-6, -4, -5)$ .