Question

Solve the system of equations: 2x+3y=-43x+2y=-1

Equations
ANSWERED
asked 2021-03-10

Solve the system of equations:
\(2x+3y=-4\)
\(3x+2y=-1\)

Answers (1)

2021-03-12

Step 1
Given,
The system of equations are
\(2x+3y=-4\)
\(3x+2y=-1\)
Step 2
Now,
The system of equations are
\(2x+3y=-4...(1)\)
\(3x+2y=-1...(2)\)
From equation (1), we have
\(\displaystyle\Rightarrow{2}{x}+{3}{y}=-{4}\)
\(\displaystyle\Rightarrow{x}={\frac{{-{4}-{3}{y}}}{{{2}}}}\)...(3)
Putting equation (3) and (2), we have
\(\displaystyle\Rightarrow{3}{\left({\frac{{-{4}-{3}{y}}}{{{2}}}}\right)}+{2}{y}=-{1}\)
\(\displaystyle\Rightarrow{\frac{{-{12}-{9}{y}+{4}{y}}}{{{2}}}}=-{1}\)
\(\displaystyle\Rightarrow-{12}-{5}{y}=-{2}\)
\(\displaystyle\Rightarrow-{5}{y}={10}\)
\(\displaystyle\Rightarrow{y}=-{2}\)
Step 3
Putting the value of y in equation (3), we have
\(\displaystyle\Rightarrow{x}={\frac{{-{4}-{3}{\left(-{2}\right)}}}{{{2}}}}\)
\(\displaystyle\Rightarrow{x}={\frac{{-{4}+{6}}}{{{2}}}}\)
\(\displaystyle\Rightarrow{x}={1}\)
\(\displaystyle\therefore\) The values of the system of equations are \(x=1\) and \(y=−2.\)

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