91Ó°ÊÓ

Equation of line in slope intercept form is expressed below.

$y=mx+c$

Where m is the slope and c is the intercept of y-axis.

Consider the first equation $2x+y=-3$.

Subtract both sides by $2x$

$\begin{array}{c}2x+y−2x=−3−2x\\ y=−3−2x\\ y=−2x−3\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $-2$ and intercept of y-axis c is $-3$.

Now, consider the second equation $6x+3y=-9$.

Strike out common factor 3 from both the sides.

$2x+y=-3$

Subtract both sides by $2x$

$\begin{array}{c}2x+y−2x=−3−2x\\ y=−3−2x\\ y=−2x−3\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $-2$ and intercept of y-axis c is $-3$.

Plot the equations on the same plane and the point where both the equations intersect is the solution of the system of the equations.

The blue line denotes the equation $2x+y=-3$ and the equation $6x+3y=-9$.

These are equivalent lines.

Therefore, all the ordered pairs that lie on the line are the solution to system of equations.

Hence, there are infinite solutions to system of equations.