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

Solve the system by substitution.\newline2x+5y=−2x=−4y−4 \begin{aligned} 2 x+5 y & =-2 \\ x & =-4 y-4 \end{aligned}

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Q. Solve the system by substitution.\newline2x+5y=−2x=−4y−4 \begin{aligned} 2 x+5 y & =-2 \\ x & =-4 y-4 \end{aligned}
  1. Identify Equation for Substitution: Identify the equation that can be used for substitution.\newlineIn the given system of equations, the second equation x=−4y−4x = -4y - 4 is already solved for xx, which makes it a good candidate for substitution.
  2. Substitute xx into First Equation: Substitute the expression for xx from the second equation into the first equation.\newlineReplace xx in 2x+5y=−22x + 5y = -2 with the expression from x=−4y−4x = -4y - 4.\newline2(−4y−4)+5y=−22(-4y - 4) + 5y = -2
  3. Distribute and Combine Terms: Distribute and combine like terms.\newline2(−4y)−2(4)+5y=−22(-4y) - 2(4) + 5y = -2\newline−8y−8+5y=−2-8y - 8 + 5y = -2\newlineCombine like terms: −8y+5y=−3y-8y + 5y = -3y\newline−3y−8=−2-3y - 8 = -2
  4. Isolate y: Isolate y by adding 88 to both sides of the equation.\newline−3y−8+8=−2+8-3y - 8 + 8 = -2 + 8\newline−3y=6-3y = 6
  5. Solve for y: Solve for y by dividing both sides by -3＂).\(\newline\$-3y / -3 = 6 / -3\)\(\newline\)\(y = -2\)
  6. Substitute \(y\) into Second Equation: Substitute the value of \(y\) back into the second equation to solve for \(x\).\[x = -4y - 4\]\[x = -4(-2) - 4\]\[x = 8 - 4\]\[x = 4\]
  7. Write Solution as Ordered Pair: Write the solution as an ordered pair \((x, y)\). The solution to the system of equations is \((4, -2)\).

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