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Solve the system of equations by substitution.\newline2x−3y−2z=−152x - 3y - 2z = -15\newline2x−2y+3z=02x - 2y + 3z = 0\newlinez=2z = 2

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Q. Solve the system of equations by substitution.\newline2x−3y−2z=−152x - 3y - 2z = -15\newline2x−2y+3z=02x - 2y + 3z = 0\newlinez=2z = 2
  1. Start with z=2z = 2: Solve the system of equations by substitution, starting with the third equation given, z=2z = 2.
  2. Substitute zz into equations: Substitute z=2z = 2 into the first two equations.\newline2x−3y−2(2)=−152x - 3y - 2(2) = -15\newline2x−2y+3(2)=02x - 2y + 3(2) = 0
  3. Simplify after substitution: Simplify the equations after substitution.\newline2x−3y−4=−152x - 3y - 4 = -15\newline2x−2y+6=02x - 2y + 6 = 0
  4. Isolate x and y terms: Add 44 to both sides of the first equation and subtract 66 from both sides of the second equation to isolate the terms with xx and yy.\newline2x−3y=−112x - 3y = -11\newline2x−2y=−62x - 2y = -6
  5. Solve for x: Now, let's solve one of the equations for xx. We can take the second equation, 2x−2y=−62x - 2y = -6, and solve for xx.\newline2x=2y−62x = 2y - 6\newlinex=y−3x = y - 3
  6. Substitute xx into equation: Substitute x=y−3x = y - 3 into the first simplified equation.2(y−3)−3y=−112(y - 3) - 3y = -11
  7. Combine like terms: Distribute and combine like terms. 2y−6−3y=−112y - 6 - 3y = -11
  8. Simplify by combining y terms: Simplify the equation by combining y terms. −y−6=−11-y - 6 = -11
  9. Solve for y: Add 66 to both sides of the equation to solve for y.\newline−y=−5-y = -5
  10. Substitute yy into xx: Multiply both sides by −1-1 to get the value of yy.y=5y = 5
  11. Calculate xx: Substitute y=5y = 5 into x=y−3x = y - 3 to find the value of xx.\newlinex=5−3x = 5 - 3
  12. Calculate xx: Substitute y=5y = 5 into x=y−3x = y - 3 to find the value of xx.x=5−3x = 5 - 3Calculate the value of xx.x=2x = 2

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