Solve the system of equations by elimination. x + 2y - 2z = -18 -3x + 2y + 2z = -2 -x + 3y - 2z = -20 ____

Eliminate z by adding equations: Add the first and second equations to eliminate z. (x + 2y - 2z) + (-3x + 2y + 2z) = -18 + (-2) -2x + 4y = -20 Divide by -2 to simplify. x - 2y = 10 Find y by dividing: Now, add the first and third equations to eliminate z. (x + 2y - 2z) + (-x + 3y - 2z) = -18 + (-20) 3y = -38 Divide by 3 to find y. y = -38 / 3 Substitute to find x: Substitute y into x - 2y = 10 to find x. x - 2(-38 / 3) = 10 x + 76/3 = 10 Multiply by 3 to clear the fraction. 3x + 76 = 30 Subtract 76 from both sides. 3x = -46 Divide by 3 to find x. x = -46 / 3 Find z by substitution: Substitute x and y into the first equation to find z. (-46 / 3) + 2(-38 / 3) - 2z = -18 Multiply by 3 to clear fractions. -46 + 2(-38) - 6z = -54 -46 - 76 - 6z = -54 Combine like terms. -122 - 6z = -54 Add 122 to both sides. -6z = 68 Divide by -6 to find z. z = 68 / -6

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Solve the system of equations by elimination. $\newline$ $x + 2y - 2z = -18$ $\newline$ $-3x + 2y + 2z = -2$ $\newline$ $-x + 3y - 2z = -20$

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Algebra 2

Solve a system of equations in three variables using elimination

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Q. Solve the system of equations by elimination.

\newline

x + 2y - 2z = -18

\newline

-3x + 2y + 2z = -2

\newline

-x + 3y - 2z = -20

Eliminate z by adding equations: Add the first and second equations to eliminate z. $\newline$ $(x + 2y - 2z) + (-3x + 2y + 2z) = -18 + (-2)$ $\newline$ $-2x + 4y = -20$ $\newline$ Divide by $-2$ to simplify. $\newline$ $x - 2y = 10$
Find $y$ by dividing: Now, add the first and third equations to eliminate $z$ . $(x + 2y - 2z) + (-x + 3y - 2z) = -18 + (-20)$ $3y = -38$ Divide by $3$ to find $y$ . $y = \frac{-38}{3}$
Substitute to find $x$ : Substitute $y$ into $x - 2y = 10$ to find $x$ .
$x - 2(-\frac{38}{3}) = 10$
$x + \frac{76}{3} = 10$
Multiply by $3$ to clear the fraction.
$3x + 76 = 30$
Subtract $76$ from both sides.
$3x = -46$
Divide by $3$ to find $x$ .
$y$ $2$
Find z by substitution: Substitute $x$ and $y$ into the first equation to find $z$ .
$(-46 / 3) + 2(-38 / 3) - 2z = -18$
Multiply by $3$ to clear fractions.
$-46 + 2(-38) - 6z = -54$
$-46 - 76 - 6z = -54$
Combine like terms.
$-122 - 6z = -54$
Add $122$ to both sides.
$-6z = 68$
Divide by $y$ $0$ to find $z$ .
$y$ $2$