Question

# Solve the system of equations 2x+3y=55x−4y=2

Systems of equations

Solve the system of equations $$2x+3y=5$$
$$5x-4y=2$$

2021-06-19

Given that $$2x+3y=5$$...(1)
and
$$5x-4y=2$$...(2).
From (1) $$\displaystyle{2}{x}={5}-{3}{y}\to{x}=\frac{{{5}-{3}{y}}}{{2}}$$. Putting this value of x in (2) we get
$$5 \times \frac{5-3y}{2}-4y=2$$
$$\rightarrow 5 \times (5-3y)-8y=4 \rightarrow -23y=-21 \rightarrow y=\frac{21}{23}$$
Therefore from (1) we have $$x=\frac{5-3y}{2} =\frac{5-3(\frac{21}{23})}{2} =\frac{115-63}{46} =\frac{26}{23}$$