Question

solve the system of equations by graphing.
x - 3y = 6
2x - y = -3

a) no solution
b) infinitely many solutions
c) (-3, -3)
d) (2, 1)

need help with this question?
get a hint

Explanation:

Step1: Rewrite equations in slope - intercept form

For $x - 3y=6$, solve for $y$:
$-3y=-x + 6$, so $y=\frac{1}{3}x - 2$.
For $2x - y=-3$, solve for $y$:
$-y=-2x - 3$, so $y = 2x+3$.

Step2: Analyze slopes and y - intercepts

The slope of $y=\frac{1}{3}x - 2$ is $m_1=\frac{1}{3}$ and y - intercept $b_1=-2$.
The slope of $y = 2x+3$ is $m_2 = 2$ and y - intercept $b_2 = 3$.
Since $m_1
eq m_2$, the lines intersect.

Step3: Check the point $(-3,-3)$

Substitute $x=-3$ and $y = - 3$ into the first equation:
Left - hand side of $x - 3y$ is $-3-3\times(-3)=-3 + 9=6$, which is equal to the right - hand side.
Substitute $x=-3$ and $y=-3$ into the second equation:
Left - hand side of $2x - y$ is $2\times(-3)-(-3)=-6 + 3=-3$, which is equal to the right - hand side.

Answer:

C. (-3, -3)