Solve the following simultaneous equations using the elimination method:
4x−3y=7
5x+2y=16
You asked:
Solve the system of equations \(4 x - 3 y = 7\), \(5 x + 2 y = 16\) by elimination.
MathBot Answer:
\[\begin{aligned}4 x - 3 y &= 7\\5 x + 2 y &= 16\end{aligned}\]
Eliminate \(x\) from equation 2 by multiply both sides of equation 1 by \(- \frac{5}{4}\), and adding the results to both sides of equation 2.
\[\begin{aligned}4 x - 3 y &= 7\\\frac{23 y}{4} &= \frac{29}{4}\end{aligned}\]
Solve equation 2 for \(y\), and substitute the solution into the remaining equations.
\[\begin{aligned}4 x &= \frac{248}{23}\\y &= \frac{29}{23}\end{aligned}\]
Solve equation 1 for the remaining unknown \(x\).
\[\begin{aligned}x &= \frac{62}{23}\\y &= \frac{29}{23}\end{aligned}\]