x+y=1 , y+z=-1 and z+x=2. What is the value of x-y-z

Identify Equations: Identify the system of equations: x + y = 1 y + z = -1 z + x = 2Solve for x: Solve for x using the first and third equations: x + y = 1 z + x = 2 Subtract the first from the third: z + x - (x + y) = 2 - 1 z - y = 1Solve for z: Solve for z using the second equation: y + z = -1 Substitute z - y = 1 into this equation: y + (1 + y) = -1 2y + 1 = -1 2y = -2 y = -1Find x: Find x using y = -1 in the first equation: x + (-1) = 1 x - 1 = 1 x = 2Find z: Find z using y = -1 in the second equation: -1 + z = -1 z = 0Calculate x - y - z: Calculate x - y - z: x - y - z = 2 - (-1) - 0 x - y - z = 3

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$x+y=1$ , $y+z=-1$ and $z+x=2$ . $\newline$ What is the value of $x-y-z$

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Math Problems

Algebra 1

Rearrange multi-variable equations

Full solution

x+y=1

y+z=-1

and

z+x=2

\newline

What is the value of

x-y-z

Identify Equations: Identify the system of equations: $\newline$ $x + y = 1$ $\newline$ $y + z = -1$ $\newline$ $z + x = 2$
Solve for x: Solve for x using the first and third equations: $\newline$ $x + y = 1$ $\newline$ $z + x = 2$ $\newline$ Subtract the first from the third: $\newline$ $z + x - (x + y) = 2 - 1$ $\newline$ $z - y = 1$
Solve for $z$ : Solve for $z$ using the second equation: $\newline$ $y + z = -1$ $\newline$ Substitute $z - y = 1$ into this equation: $\newline$ $y + (1 + y) = -1$ $\newline$ $2y + 1 = -1$ $\newline$ $2y = -2$ $\newline$ $y = -1$
Find x: Find x using $y = -1$ in the first equation: $\newline$ $x + (-1) = 1$ $\newline$ $x - 1 = 1$ $\newline$ $x = 2$
Find $z$ : Find $z$ using $y = -1$ in the second equation: $\newline$ $-1 + z = -1$ $\newline$ $z = 0$
Calculate $x - y - z$ : Calculate $x - y - z$ : $x - y - z = 2 - (-1) - 0$ $x - y - z = 3$