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\. \\(\

$$\begin{cases} 6x - 3y = -27 \\\\ x + y = 3 \\end{cases}$$

\\) show your work here

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(6x - 3y=-27\), we solve for \(y\):
Subtract \(6x\) from both sides: \(-3y=-6x - 27\)
Divide both sides by \(-3\): \(y = 2x+9\)

For the second equation \(x + y=3\), we solve for \(y\):
Subtract \(x\) from both sides: \(y=-x + 3\)

Step2: Find intersection point

To find the solution of the system, we set the two equations equal to each other since the \(y\) - values at the intersection point are the same:
\(2x + 9=-x+3\)
Add \(x\) to both sides: \(2x+x+9=-x+x + 3\), which simplifies to \(3x+9 = 3\)
Subtract 9 from both sides: \(3x+9 - 9=3 - 9\), so \(3x=-6\)
Divide both sides by 3: \(x=\frac{-6}{3}=-2\)

Now substitute \(x = - 2\) into the equation \(y=-x + 3\):
\(y=-(-2)+3=2 + 3=5\)

Answer:

\((-2,5)\)