Solve the system of equations by substitution. 2x - 2y - 2z = 2 x = 7 -3x + 3y + z = -9 ____

Substitute x = 7: First, let's substitute x = 7 into the other two equations. 2(7) - 2y - 2z = 2 -3(7) + 3y + z = -9Simplify equations: Now, let's simplify both equations. 14 - 2y - 2z = 2 -21 + 3y + z = -9Solve for y in first equation: Next, we'll solve the first equation for y. 14 - 2y - 2z = 2 -2y - 2z = 2 - 14 -2y - 2z = -12Divide by -2 for y: Divide the whole equation by -2 to solve for y. y + z = 6Solve for y in second equation: Now, let's solve the second equation for y. -21 + 3y + z = -9 3y + z = -9 + 21 3y + z = 12Divide by 3 for y: Divide the whole equation by 3 to solve for y. y + z/3 = 4 Oops, this step contains a mistake. We should not divide z by 3 when dividing the whole equation by 3.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system of equations by substitution. $\newline$ $2x - 2y - 2z = 2$ $\newline$ $x = 7$ $\newline$ $-3x + 3y + z = -9$

View step-by-step help

Home

Math Problems

Precalculus

Solve a system of equations in three variables using substitution

Full solution

Q. Solve the system of equations by substitution.

\newline

2x - 2y - 2z = 2

\newline

x = 7

\newline

-3x + 3y + z = -9

Substitute $x = 7$ : First, let's substitute $x = 7$ into the other two equations. $\newline$ $2(7) - 2y - 2z = 2$ $\newline$ $-3(7) + 3y + z = -9$
Simplify equations: Now, let's simplify both equations. $\newline$ $14 - 2y - 2z = 2$ $\newline$ $-21 + 3y + z = -9$
Solve for y in first equation: Next, we'll solve the first equation for y. $\newline$ $14 - 2y - 2z = 2$ $\newline$ $-2y - 2z = 2 - 14$ $\newline$ $-2y - 2z = -12$
Divide by $-2$ for $y$ : Divide the whole equation by $-2$ to solve for $y$ . $y + z = 6$
Solve for y in second equation: Now, let's solve the second equation for y. $\newline$ $-21 + 3y + z = -9$ $\newline$ $3y + z = -9 + 21$ $\newline$ $3y + z = 12$
Divide by $3$ for y: Divide the whole equation by $3$ to solve for y. $\newline$ $y + \frac{z}{3} = 4$ $\newline$ Oops, this step contains a mistake. We should not divide $z$ by $3$ when dividing the whole equation by $3$ .