Step 1

Given: The system of equations

3x−y=−2

\(\displaystyle{2}{x}^{{2}}−{y}={0}\)

To find: The solution of given system of equation.

Step 2

Explanation:

Let

3x−y=−2 ...(i)

\(\displaystyle{2}{x}^{{2}}−{y}={0}\) ...(ii),

From equation (i),

3x−y=−2,

\(\displaystyle\Rightarrow{y}={3}{x}+{2}\)

Substituting y=3x+2 in equation (ii),

\(\displaystyle{2}{x}^{{2}}-{y}={0}\)

\(\displaystyle\Rightarrow{2}{x}^{{2}}-{\left({3}{x}+{2}\right)}={0}\)

\(\displaystyle\Rightarrow{2}{x}^{{2}}-{3}{x}-{2}={0}\)

\(\displaystyle\Rightarrow{2}{x}^{{2}}-{4}{x}+{x}-{2}={0}\)

\(\displaystyle\Rightarrow{\left({x}-{2}\right)}{\left({2}{x}+{1}\right)}={0}\)

\(\displaystyle\Rightarrow{x}={2},-\frac{{1}}{{2}}\)

Now,

For \(\displaystyle{x}={2},{y}={3}\times{2}+{2}={8}\),

For \(\displaystyle{x}=-\frac{{1}}{{2}},{y}={3}\times{\left(-\frac{{1}}{{2}}\right)}+{2}=-\frac{{3}}{{2}}+{2}=\frac{{1}}{{2}}\)

Hence x=2, y=8 and \(\displaystyle{x}=−\frac{{1}}{{2}},{y}=\frac{{1}}{{2}}\) are solution of given system of equations.

Result: x=2, y=8 and \(\displaystyle{x}=−\frac{{1}}{{2}},{y}=\frac{{1}}{{2}}\) are solution of given system of equation.

Given: The system of equations

3x−y=−2

\(\displaystyle{2}{x}^{{2}}−{y}={0}\)

To find: The solution of given system of equation.

Step 2

Explanation:

Let

3x−y=−2 ...(i)

\(\displaystyle{2}{x}^{{2}}−{y}={0}\) ...(ii),

From equation (i),

3x−y=−2,

\(\displaystyle\Rightarrow{y}={3}{x}+{2}\)

Substituting y=3x+2 in equation (ii),

\(\displaystyle{2}{x}^{{2}}-{y}={0}\)

\(\displaystyle\Rightarrow{2}{x}^{{2}}-{\left({3}{x}+{2}\right)}={0}\)

\(\displaystyle\Rightarrow{2}{x}^{{2}}-{3}{x}-{2}={0}\)

\(\displaystyle\Rightarrow{2}{x}^{{2}}-{4}{x}+{x}-{2}={0}\)

\(\displaystyle\Rightarrow{\left({x}-{2}\right)}{\left({2}{x}+{1}\right)}={0}\)

\(\displaystyle\Rightarrow{x}={2},-\frac{{1}}{{2}}\)

Now,

For \(\displaystyle{x}={2},{y}={3}\times{2}+{2}={8}\),

For \(\displaystyle{x}=-\frac{{1}}{{2}},{y}={3}\times{\left(-\frac{{1}}{{2}}\right)}+{2}=-\frac{{3}}{{2}}+{2}=\frac{{1}}{{2}}\)

Hence x=2, y=8 and \(\displaystyle{x}=−\frac{{1}}{{2}},{y}=\frac{{1}}{{2}}\) are solution of given system of equations.

Result: x=2, y=8 and \(\displaystyle{x}=−\frac{{1}}{{2}},{y}=\frac{{1}}{{2}}\) are solution of given system of equation.