Question

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

Systems of equations
ANSWERED
asked 2021-06-18

Solve the system of equations \(2x+3y=5\)
\(5x-4y=2\)

Answers (1)

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 \(x=\frac{5-3y}{2} =\frac{5-3(\frac{21}{23})}{2} =\frac{115-63}{46} =\frac{26}{23}\)

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