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Solve the system by substitution. {:[-7x+y=26],[y=-6x]:}

Solve the system by substitution.\newline−7x+y=26y=−6x \begin{aligned} -7 x+y & =26 \\ y & =-6 x \end{aligned}

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Q. Solve the system by substitution.\newline−7x+y=26y=−6x \begin{aligned} -7 x+y & =26 \\ y & =-6 x \end{aligned}
  1. Substitute yy into first equation: Substitute the expression for yy from the second equation into the first equation.\newlineGiven y=−6xy = -6x, we can substitute this into the first equation −7x+y=26-7x + y = 26.\newline−7x+(−6x)=26-7x + (-6x) = 26
  2. Combine like terms: Combine like terms and solve for xx.−7x−6x=26-7x - 6x = 26−13x=26-13x = 26
  3. Solve for x: Divide both sides by −13-13 to find the value of x.\newlinex=26−13x = \frac{26}{-13}\newlinex=−2x = -2
  4. Substitute xx into second equation: Substitute the value of xx back into the second equation to find yy.y=−6xy = -6xy=−6(−2)y = -6(-2)y=12y = 12
  5. Write solution as ordered pair: Write the solution as an ordered pair (x,y)(x, y). The solution is (−2,12)(-2, 12).

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