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

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Q. Solve the system of equations by substitution.\newline−x+2y−z=17-x + 2y - z = 17\newline−2x+y+z=4-2x + y + z = 4\newlinex=1x = 1
  1. Substitute x=1x = 1: Substitute x=1x = 1 into the first equation −x+2y−z=17-x + 2y - z = 17.\newline−1+2y−z=17-1 + 2y - z = 17\newline2y−z=182y - z = 18
  2. Substitute x=1x = 1: Substitute x=1x = 1 into the second equation −2x+y+z=4-2x + y + z = 4.\newline−2(1)+y+z=4-2(1) + y + z = 4\newline−2+y+z=4-2 + y + z = 4\newliney+z=6y + z = 6
  3. Solve system of equations: Solve the system of equations formed by 2y−z=182y - z = 18 and y+z=6y + z = 6. We can add the two equations to eliminate zz. (2y−z)+(y+z)=18+6(2y - z) + (y + z) = 18 + 6 2y+y=242y + y = 24 3y=243y = 24
  4. Find value of y: Divide both sides by 33 to find the value of y.\newline3y3=243\frac{3y}{3} = \frac{24}{3}\newliney=8y = 8
  5. Find value of zz: Substitute y=8y = 8 into y+z=6y + z = 6 to find the value of zz.8+z=68 + z = 6z=6−8z = 6 - 8z=−2z = -2

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