Solve the system of equations by substitution. 2x - 3y - 2z = -15 2x - 2y + 3z = 0 z = 2 ____

Start with z = 2: Solve the system of equations by substitution, starting with the third equation given, z = 2.Substitute z into equations: Substitute z = 2 into the first two equations. 2x - 3y - 2(2) = -15 2x - 2y + 3(2) = 0Simplify after substitution: Simplify the equations after substitution. 2x - 3y - 4 = -15 2x - 2y + 6 = 0Isolate x and y terms: Add 4 to both sides of the first equation and subtract 6 from both sides of the second equation to isolate the terms with x and y. 2x - 3y = -11 2x - 2y = -6Solve for x: Now, let's solve one of the equations for x. We can take the second equation, 2x - 2y = -6, and solve for x. 2x = 2y - 6 x = y - 3Substitute x into equation: Substitute x = y - 3 into the first simplified equation. 2(y - 3) - 3y = -11Combine like terms: Distribute and combine like terms. 2y - 6 - 3y = -11Simplify by combining y terms: Simplify the equation by combining y terms. -y - 6 = -11Solve for y: Add 6 to both sides of the equation to solve for y. -y = -5Substitute y into x: Multiply both sides by -1 to get the value of y. y = 5Calculate x: Substitute y = 5 into x = y - 3 to find the value of x. x = 5 - 3Calculate the value of x. x = 2

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Solve the system of equations by substitution. $\newline$ $2x - 3y - 2z = -15$ $\newline$ $2x - 2y + 3z = 0$ $\newline$ $z = 2$

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Precalculus

Solve a system of equations in three variables using substitution

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Q. Solve the system of equations by substitution.

\newline

2x - 3y - 2z = -15

\newline

2x - 2y + 3z = 0

\newline

z = 2

Start with $z = 2$ : Solve the system of equations by substitution, starting with the third equation given, $z = 2$ .
Substitute $z$ into equations: Substitute $z = 2$ into the first two equations. $\newline$ $2x - 3y - 2(2) = -15$ $\newline$ $2x - 2y + 3(2) = 0$
Simplify after substitution: Simplify the equations after substitution. $\newline$ $2x - 3y - 4 = -15$ $\newline$ $2x - 2y + 6 = 0$
Isolate x and y terms: Add $4$ to both sides of the first equation and subtract $6$ from both sides of the second equation to isolate the terms with $x$ and $y$ . $\newline$ $2x - 3y = -11$ $\newline$ $2x - 2y = -6$
Solve for x: Now, let's solve one of the equations for $x$ . We can take the second equation, $2x - 2y = -6$ , and solve for $x$ . $\newline$ $2x = 2y - 6$ $\newline$ $x = y - 3$
Substitute $x$ into equation: Substitute $x = y - 3$ into the first simplified equation. $2(y - 3) - 3y = -11$
Combine like terms: Distribute and combine like terms. $2y - 6 - 3y = -11$
Simplify by combining y terms: Simplify the equation by combining y terms. $-y - 6 = -11$
Solve for y: Add $6$ to both sides of the equation to solve for y. $\newline$ $-y = -5$
Substitute $y$ into $x$ : Multiply both sides by $-1$ to get the value of $y$ . $y = 5$
Calculate $x$ : Substitute $y = 5$ into $x = y - 3$ to find the value of $x$ . $\newline$ $x = 5 - 3$
Calculate $x$ : Substitute $y = 5$ into $x = y - 3$ to find the value of $x$ . $x = 5 - 3$ Calculate the value of $x$ . $x = 2$