Q46. - Algebra 2

Question

Solve each system of equations by graphing.

 

 $\begin{array}{c}46.2x+y=-3\\ 6x+3y=-9\end{array}$

Step-by-Step Solution

Answer

There are infinite solutions to the system of equations.

Step-1 – Apply the concept of slope-intercept form

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.

Step-2 –Write the equations in slope-intercept form

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 $-3$.

Step-3 – Identify the point of intersection of the equations

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.