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Find the solution to the system by the substitution method. Check your answers. {:[5x+8y=10],[x+2y=-2]:}

Find the solution to the system by the substitution method. Check your answers.\newline5x+8y=10x+2y=−2 \begin{aligned} 5 x+8 y & =10 \\ x+2 y & =-2 \end{aligned}

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Full solution

Q. Find the solution to the system by the substitution method. Check your answers.\newline5x+8y=10x+2y=−2 \begin{aligned} 5 x+8 y & =10 \\ x+2 y & =-2 \end{aligned}
  1. Solve for x: Solve the second equation for x:\newlinex+2y=−2x + 2y = -2\newlinex=−2−2yx = -2 - 2y
  2. Substitute x: Substitute x in the first equation:\newline5x+8y=105x + 8y = 10\newline5(−2−2y)+8y=105(-2 - 2y) + 8y = 10\newline−10−10y+8y=10-10 - 10y + 8y = 10\newline−2y=20-2y = 20
  3. Solve for y: Solve for y:\newline−2y=20-2y = 20\newliney=−10y = -10
  4. Substitute yy into xx: Substitute yy back into the equation for xx:
    x=−2−2(−10)x = -2 - 2(-10)
    x=−2+20x = -2 + 20
    x=18x = 18
  5. Check solution: Check the solution by substituting xx and yy into both original equations:\newlineFirst equation: 5x+8y=105x + 8y = 10\newline5(18)+8(−10)=90−80=105(18) + 8(-10) = 90 - 80 = 10\newlineSecond equation: x+2y=−2x + 2y = -2\newline18+2(−10)=18−20=−218 + 2(-10) = 18 - 20 = -2\newlineBoth equations are satisfied.

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