Solve the system of equations by substitution. 2x + y - 3z = -20 x = -1 x - 3y - 3z = 5 ____

Substitute x = -1: Substitute x = -1 into 2x + y - 3z = -20. Calculation: 2(-1) + y - 3z = -20 -2 + y - 3z = -20 y - 3z = -18Substitute x = -1: Substitute x = -1 into x - 3y - 3z = 5. Calculation: (-1) - 3y - 3z = 5 -1 - 3y - 3z = 5 -3y - 3z = 6Divide second equation: Divide the second equation by -3 to simplify. Calculation: (-3y - 3z) / -3 = 6 / -3 y + z = -2Substitute z from: Substitute z from y + z = -2 into y - 3z = -18. Calculation: y - 3(-2 - y) = -18 y + 6 + 3y = -18 4y + 6 = -18Subtract 6: Subtract 6 from both sides to solve for y. Calculation: 4y = -18 - 6 4y = -24 y = -24 / 4 y = -6Substitute y = -6: Substitute y = -6 into y + z = -2 to find z. Calculation: -6 + z = -2 z = -2 + 6 z = 4Check values satisfy: We have x = -1, y = -6, and z = 4. Check if these values satisfy the original equations. For 2x + y - 3z = -20: 2(-1) + (-6) - 3(4) = -20 -2 - 6 - 12 = -20 -20 = -20 (Correct) For x - 3y - 3z = 5: (-1) - 3(-6) - 3(4) = 5 -1 + 18 - 12 = 5 5 = 5 (Correct)

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Solve the system of equations by substitution. $\newline$ $2x + y - 3z = -20$ $\newline$ $x = -1$ $\newline$ $x - 3y - 3z = 5$

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Algebra 2

Solve a system of equations in three variables using substitution

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Q. Solve the system of equations by substitution.

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2x + y - 3z = -20

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x = -1

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x - 3y - 3z = 5

Substitute $x = -1$ : Substitute $x = -1$ into $2x + y - 3z = -20$ . $\newline$ Calculation: $2(-1) + y - 3z = -20$ $\newline$ $-2 + y - 3z = -20$ $\newline$ $y - 3z = -18$
Substitute $x = -1$ : Substitute $x = -1$ into $x - 3y - 3z = 5$ . $\newline$ Calculation: $(-1) - 3y - 3z = 5$ $\newline$ $-1 - 3y - 3z = 5$ $\newline$ $-3y - 3z = 6$
Divide second equation: Divide the second equation by $-3$ to simplify. $\newline$ Calculation: $\frac{-3y - 3z}{-3} = \frac{6}{-3}$ $\newline$ y + z = $-2$
Substitute $z$ from: Substitute $z$ from $y + z = -2$ into $y - 3z = -18$ . $\newline$ Calculation: $y - 3(-2 - y) = -18$ $\newline$ $y + 6 + 3y = -18$ $\newline$ $4y + 6 = -18$
Subtract $6$ : Subtract $6$ from both sides to solve for $y$ . $\newline$ Calculation: $4y = -18 - 6$ $\newline$ $4y = -24$ $\newline$ $y = -24 / 4$ $\newline$ $y = -6$
Substitute $y = -6$ : Substitute $y = -6$ into $y + z = -2$ to find $z$ . $\newline$ Calculation: $-6 + z = -2$ $\newline$ $z = -2 + 6$ $\newline$ $z = 4$
Check values satisfy: We have $x = -1$ , $y = -6$ , and $z = 4$ . Check if these values satisfy the original equations. For $2x + y - 3z = -20$ : $2(-1) + (-6) - 3(4) = -20$ $-2 - 6 - 12 = -20$ $-20 = -20$ (Correct) For $x - 3y - 3z = 5$ : $(-1) - 3(-6) - 3(4) = 5$ $-1 + 18 - 12 = 5$ $y = -6$ $0$ (Correct)