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Find the solution to the system by the substitution method. Check your answers. {:[3x+4y=10],[x+2y=-2]:}

Find the solution to the system by the substitution method. Check your answers.\newline3x+4y=10x+2y=−2 \begin{array}{r} 3 x+4 y=10 \\ x+2 y=-2 \end{array}

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Full solution

Q. Find the solution to the system by the substitution method. Check your answers.\newline3x+4y=10x+2y=−2 \begin{array}{r} 3 x+4 y=10 \\ x+2 y=-2 \end{array}
  1. Solve for x: Step 11: Solve the second equation for x.\newlineGiven equation: x+2y=−2x + 2y = -2\newlineSolve for x: x=−2−2yx = -2 - 2y
  2. Substitute xx: Step 22: Substitute xx in the first equation.\newlineSubstitute x=−2−2yx = -2 - 2y into 3x+4y=103x + 4y = 10:\newline3(−2−2y)+4y=103(-2 - 2y) + 4y = 10\newline−6−6y+4y=10-6 - 6y + 4y = 10\newline−2y=16-2y = 16
  3. Solve for y: Step 33: Solve for y.\newlineDivide both sides by −2-2: y=−8y = -8
  4. Substitute yy into xx: Step 44: Substitute yy back into the equation for xx.x=−2−2(−8)x = -2 - 2(-8)x=−2+16x = -2 + 16x=14x = 14
  5. Check solution: Step 55: Check the solution by substituting xx and yy back into the original equations.\newlineCheck in first equation: 3(14)+4(−8)=42−32=103(14) + 4(-8) = 42 - 32 = 10\newlineCheck in second equation: 14+2(−8)=14−16=−214 + 2(-8) = 14 - 16 = -2\newlineBoth checks are correct.

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