Solve the system of equations by substitution. -x + 2y - z = 17 -2x + y + z = 4 x = 1 ____

Substitute x = 1: Substitute x = 1 into the first equation -x + 2y - z = 17. -1 + 2y - z = 17 2y - z = 18Substitute x = 1: Substitute x = 1 into the second equation -2x + y + z = 4. -2(1) + y + z = 4 -2 + y + z = 4 y + z = 6Solve system of equations: Solve the system of equations formed by 2y - z = 18 and y + z = 6. We can add the two equations to eliminate z. (2y - z) + (y + z) = 18 + 6 2y + y = 24 3y = 24Find value of y: Divide both sides by 3 to find the value of y. 3y / 3 = 24 / 3 y = 8Find value of z: Substitute y = 8 into y + z = 6 to find the value of z. 8 + z = 6 z = 6 - 8 z = -2

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Solve the system of equations by substitution. $\newline$ $-x + 2y - z = 17$ $\newline$ $-2x + y + z = 4$ $\newline$ $x = 1$

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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.

\newline

-x + 2y - z = 17

\newline

-2x + y + z = 4

\newline

x = 1

Substitute $x = 1$ : Substitute $x = 1$ into the first equation $-x + 2y - z = 17$ . $\newline$ $-1 + 2y - z = 17$ $\newline$ $2y - z = 18$
Substitute $x = 1$ : Substitute $x = 1$ into the second equation $-2x + y + z = 4$ . $\newline$ $-2(1) + y + z = 4$ $\newline$ $-2 + y + z = 4$ $\newline$ $y + z = 6$
Solve system of equations: Solve the system of equations formed by $2y - z = 18$ and $y + z = 6$ . We can add the two equations to eliminate $z$ . $(2y - z) + (y + z) = 18 + 6$ $2y + y = 24$ $3y = 24$
Find value of y: Divide both sides by $3$ to find the value of y. $\newline$ $\frac{3y}{3} = \frac{24}{3}$ $\newline$ $y = 8$
Find value of $z$ : Substitute $y = 8$ into $y + z = 6$ to find the value of $z$ . $8 + z = 6$ $z = 6 - 8$ $z = -2$