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: Simplify the first equation

Divide the first equation \(15x - 5y = -45\) by 5: \(3x - y = -9\), so \(y = 3x + 9\).

Step2: Simplify the second equation

Rewrite the second equation \(2x - y = -5\) as \(y = 2x + 5\).

Step3: Analyze the slopes and intercepts

The first line has a slope of 3 and y - intercept 9. The second line has a slope of 2 and y - intercept 5. Since the slopes are different, the two lines intersect at one point.

Step4: Solve the system algebraically (to find the intersection)

Set the two expressions for \(y\) equal: \(3x + 9 = 2x + 5\).
Subtract \(2x\) from both sides: \(x+9 = 5\).
Subtract 9 from both sides: \(x = 5 - 9=-4\).
Substitute \(x = - 4\) into \(y = 2x+5\): \(y=2\times(-4)+5=-8 + 5=-3\).

Answer:

The solution is the ordered pair \((-4,-3)\)