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Solve the system by substitution. {:[y=5x+2],[-3x+4y=-26]:}

Solve the system by substitution.\newliney=5x+2−3x+4y=−26 \begin{aligned} y & =5 x+2 \\ -3 x+4 y & =-26 \end{aligned}

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Q. Solve the system by substitution.\newliney=5x+2−3x+4y=−26 \begin{aligned} y & =5 x+2 \\ -3 x+4 y & =-26 \end{aligned}
  1. Substitute yy: Substitute yy from the first equation into the second equation.\newlineGiven the first equation y=5x+2y = 5x + 2, we can substitute yy in the second equation −3x+4y=−26-3x + 4y = -26.
  2. Replace yy: Replace yy in the second equation with 5x+25x + 2.\newline−3x+4(5x+2)=−26-3x + 4(5x + 2) = -26
  3. Distribute 44: Distribute 44 across the terms inside the parentheses.\newline−3x+20x+8=−26-3x + 20x + 8 = -26
  4. Combine like terms: Combine like terms. 17x+8=−2617x + 8 = -26
  5. Subtract 88: Subtract 88 from both sides to isolate the term with xx.\newline17x=−26−817x = -26 - 8
  6. Calculate right side: Calculate the right side of the equation. 17x=−3417x = -34
  7. Divide both sides: Divide both sides by 1717 to solve for xx.\newlinex=−3417x = -\frac{34}{17}
  8. Simplify fraction: Simplify the fraction to find the value of xx.x=−2x = -2
  9. Substitute xx back: Substitute xx back into the first equation to solve for yy.y=5(−2)+2y = 5(-2) + 2
  10. Calculate value of y: Calculate the value of yy.y=−10+2y = -10 + 2
  11. Simplify to find yy: Simplify to find the value of yy.y=−8y = -8
  12. Write solution as ordered pair: Write the solution as an ordered pair (x,y)(x, y).\newlineThe solution is (−2,−8)(-2, -8).

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