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Solve the system by substitution. {:[y=-4x+5],[8x-2y=-42]:}

Solve the system by substitution.\newliney=−4x+58x−2y=−42 \begin{aligned} y & =-4 x+5 \\ 8 x-2 y & =-42 \end{aligned}

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Q. Solve the system by substitution.\newliney=−4x+58x−2y=−42 \begin{aligned} y & =-4 x+5 \\ 8 x-2 y & =-42 \end{aligned}
  1. Substitute yy in second equation: Substitute the expression for yy from the first equation into the second equation.\newlineGiven the first equation y=−4x+5y = -4x + 5, we can substitute this into the second equation 8x−2y=−428x - 2y = -42.
  2. Perform the substitution: Perform the substitution. 8x−2(−4x+5)=−428x - 2(-4x + 5) = -42
  3. Distribute and simplify: Distribute the −2-2 across the parentheses.8x+8x−10=−428x + 8x - 10 = -42
  4. Combine like terms: Combine like terms. 16x−10=−4216x - 10 = -42
  5. Isolate x term: Add 1010 to both sides of the equation to isolate the term with xx.\newline16x−10+10=−42+1016x - 10 + 10 = -42 + 10\newline16x=−3216x = -32
  6. Solve for x: Divide both sides by 1616 to solve for x.\newline16x16=−3216\frac{16x}{16} = \frac{-32}{16}\newlinex=−2x = -2
  7. Substitute xx back into first equation: Substitute the value of xx back into the first equation to solve for yy.y=−4(−2)+5y = -4(-2) + 5
  8. Perform multiplication and addition: Perform the multiplication and addition to find yy.y=8+5y = 8 + 5y=13y = 13
  9. Write solution as ordered pair: Write the solution as an ordered pair (x,y)(x, y).\newlineThe solution is (−2,13)(-2, 13).

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