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Solve using elimination: \newline5x+4y=−9, 4x−3y=305x+4y=-9, \ 4x-3y=30

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Q. Solve using elimination: \newline5x+4y=−9, 4x−3y=305x+4y=-9, \ 4x-3y=30
  1. Align Equations for Elimination: Step 11: Align the equations for elimination.\newlineEquations given:\newline11) 5x+4y=−95x + 4y = -9\newline22) 4x−3y=304x - 3y = 30\newlineWe aim to eliminate one variable by making the coefficients of yy equal in magnitude but opposite in sign.
  2. Multiply to Align Coefficients: Step 22: Multiply the first equation by 33 and the second by 44 to align the yy coefficients.\newline(5x+4y)×3=−9×3→15x+12y=−27(5x + 4y) \times 3 = -9 \times 3 \rightarrow 15x + 12y = -27\newline(4x−3y)×4=30×4→16x−12y=120(4x - 3y) \times 4 = 30 \times 4 \rightarrow 16x - 12y = 120\newlineNow, the yy coefficients are 1212 and −12-12, which can be eliminated by addition.
  3. Add Equations to Eliminate: Step 33: Add the modified equations to eliminate yy.\newline15x+12y+16x−12y=−27+12015x + 12y + 16x - 12y = -27 + 120\newline31x=9331x = 93\newlineNow, solve for xx:\newlinex=9331x = \frac{93}{31}\newlinex=3x = 3
  4. Substitute and Solve: Step 44: Substitute x=3x = 3 back into one of the original equations to find yy. Using the first equation: 5x+4y=−95x + 4y = -9 5(3)+4y=−95(3) + 4y = -9 15+4y=−915 + 4y = -9 4y=−9−154y = -9 - 15 4y=−244y = -24 y=−24/4y = -24 / 4 y=−6y = -6

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