Question

solve for x and y by graphing the system of linear equations. drag the points to move the lines on the graph. then write the solution as an ordered pair. if no solution exists, write
o solution\. if infinite solutions exist, write \infinite solutions\.
\

$$\begin{cases} 15x - 5y = -45 \\\\ 2x - y = -5 \\end{cases}$$

show your work here

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(15x - 5y=-45\), we solve for \(y\):
Subtract \(15x\) from both sides: \(- 5y=-15x - 45\)
Divide both sides by \(-5\): \(y = 3x+9\)

For the second equation \(2x - y=-5\), we solve for \(y\):
Subtract \(2x\) from both sides: \(-y=-2x - 5\)
Multiply both sides by \(-1\): \(y = 2x + 5\)

Step2: Analyze the slopes and y - intercepts

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
For the line \(y = 3x+9\), the slope \(m_1 = 3\) and the y - intercept \(b_1=9\).
For the line \(y = 2x + 5\), the slope \(m_2 = 2\) and the y - intercept \(b_2 = 5\).
Since the slopes \(m_1
eq m_2\), the two lines are not parallel and will intersect at a single point.

Step3: Find the intersection point (solve the system)

We can also solve the system by substitution or elimination. Let's use elimination.
Multiply the second equation \(2x - y=-5\) by \(5\) to get \(10x-5y=-25\).
Now we have the system:
\(

$$\begin{cases}15x - 5y=-45\\10x-5y=-25\end{cases}$$

\)
Subtract the second equation from the first equation:
\((15x-5y)-(10x - 5y)=-45-(-25)\)
\(15x-5y - 10x + 5y=-45 + 25\)
\(5x=-20\)
Divide both sides by \(5\): \(x=-4\)

Substitute \(x = - 4\) into the second equation \(2x-y=-5\):
\(2(-4)-y=-5\)
\(-8 - y=-5\)
Add \(8\) to both sides: \(-y=-5 + 8=3\)
Multiply both sides by \(-1\): \(y=-3\)

Answer:

\((-4,-3)\)