7x + y = 5
2x - 5y = -62
solve the linear equations by elimination
You asked:
Solve the system of equations \(7 x + y = 5\), \(2 x - 5 y = -62\) by elimination.
MathBot Answer:
\[\begin{aligned}x &= -1\\y &= 12\end{aligned}\]
\[\begin{aligned}7 x + y &= 5\\2 x - 5 y &= -62\end{aligned}\]
Eliminate \(x\) from equation 2 by multiply both sides of equation 1 by \(- \frac{2}{7}\), and adding the results to both sides of equation 2.
\[\begin{aligned}7 x + y &= 5\\- \frac{37 y}{7} &= - \frac{444}{7}\end{aligned}\]
Solve equation 2 for \(y\), and substitute the solution into the remaining equations.
\[\begin{aligned}7 x &= -7\\y &= 12\end{aligned}\]
Solve equation 1 for the remaining unknown \(x\).
\[\begin{aligned}x &= -1\\y &= 12\end{aligned}\]