Q48. - Algebra 2

Question

Solve each system of equations by graphing.

48.

$\begin{array}{l}\mathbf{y}=\mathbf{3}\mathbf{x}+\mathbf{5}\\ \mathbf{y}=-\mathbf{2}\mathbf{x}-\mathbf{5}\end{array}$

Step-by-Step Solution

Answer

The solution of system of equations is $\mathbf{x}\mathbf{=}\mathbf{-}\mathbf{2}$ and $\mathbf{y}\mathbf{=}\mathbf{-}\mathbf{1}$.

Step 1 ­- Description of step.

Number the given system of equations.

$\begin{array}{l}y=3x+5\left(1\right)\\ y=-2x-5\left(2\right)\end{array}$

Step 2 ­- Description of step.

The first equation is: $y=3x+5$.

When $x=0$,

$\begin{array}{l}y=3\left(0\right)+5\\ =0+5\\ =5\end{array}$

Therefore, when $x=0$, $y=5$.

When $x=-1$,

$\begin{array}{l}y=3\left(-1\right)+5\\ =-3+5\\ =2\end{array}$

Therefore, when $x=-1$, $y=2$

Therefore, the equation $y=3x+5$ is the equation of the line passing through the points $\left(0,5\right)$ and $\left(-1,2\right)$.

Step 3 ­- Graph the equation y = 3 x + 5 .

The graph of the equation $y=3x+5$ is:

Step 4 ­- Description of step.

The second equation is: $y=-2x-5$.

When $x=0$,

$\begin{array}{l}y=-2\left(0\right)-5\\ =-0-5\\ =-5\end{array}$

Therefore, when $x=0$, $y=-5$.

When $x=-1$,

$\begin{array}{l}y=-2\left(-1\right)-5\\ =2-5\\ =-3\end{array}$

Therefore, when $x=-1$, $y=-3$

Therefore, the equation $y=-2x-5$ is the equation of the line passing through the points $\left(0,-5\right)$ and $\left(-1,-3\right)$.

Step 5 ­- Graph the equation y = - 2 x - 5 .

The graph of the equation $y=-2x-5$ is:

Step 6 ­- Graph the equations y = 3 x + 5 and y = - 2 x - 5 .

The graph of the equations $y=3x+5$ and $y=-2x-5$ is:

Step 7 ­- Description of step.

From the graph of the equations $y=3x+5$ and $y=-2x-5$, it can be noticed that the lines are intersecting at a point $\left(-2,-1\right)$.

The solution of the system of linear equations in two variables is given by the intersection point of the lines.

Therefore, the solution of the given system of equations is $\left(-2,-1\right)$.

That implies, the solution of the given system of equation is $x=-2$ and $y=-1$.