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7x+10y=60 7x−2y=240\begin{aligned} 7x+10y&=60 \ 7x-2y&=240 \end{aligned}

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Full solution

Q. 7x+10y=60 7x−2y=240\begin{aligned} 7x+10y&=60 \ 7x-2y&=240 \end{aligned}
  1. Elimination Method: To solve the system of equations, we can use the method of elimination or substitution. Since the coefficients of xx in both equations are the same, elimination seems to be a good strategy. We will subtract the second equation from the first to eliminate xx.
  2. Subtract Equations: Subtract the second equation from the first:\newline(7x+10y)−(7x−2y)=60−240(7x + 10y) - (7x - 2y) = 60 - 240\newlineThis simplifies to:\newline7x+10y−7x+2y=−1807x + 10y - 7x + 2y = -180
  3. Combine Like Terms: Combine like terms:\newline10y+2y=−18010y + 2y = -180\newline12y=−18012y = -180
  4. Solve for y: Divide both sides by 1212 to solve for y:\newliney = −180/12-180 / 12\newliney = −15-15
  5. Substitute into Equation: Now that we have the value of yy, we can substitute it back into one of the original equations to solve for xx. We'll use the first equation: 7x+10(−15)=607x + 10(-15) = 60
  6. Solve for x: Solve for x:\newline7x−150=607x - 150 = 60\newline7x=60+1507x = 60 + 150\newline7x=2107x = 210
  7. Final Solution: Divide both sides by 77 to find the value of x:\newlinex=2107x = \frac{210}{7}\newlinex=30x = 30

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