Question

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

Equations

Solve the system of equations:
$$2x+3y=-4$$
$$3x+2y=-1$$

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 $$y=−2.$$