Answer
Parallel
Work Step by Step
To solve this system of equations, we use the graphing method.
$2x+y=6$
$y=-2x+1$
Taking the first equation, we solve for y.
$2x+y=6$
$y=6-2x$
Find three solutions:
For x=2,
$y=6-2x$
$y=6-2(2)$
$y=6-4$
$y=2$
For x=0,
$y=6-2x$
$y=6-2(0)$
$y=6-0=6$
For x=-2,
$y=6-2x$
$y=6-2(-2)$
$y=6+4=10$
With the three points, $(2,2), (0,6), (-2,10)$, we can graph the straight line that goes through these points.
Taking the second equation, we find three solutions:
For x=2,
$y=-2x+1$
$y=-2(2)+1$
$y=-4+1=-3$
For x=0,
$y=-2x+1$
$y=-2(0)+1$
$y=0+1=1$
For x=-2,
$y=-2x+1$
$y=-2(-2)+1$
$y=4+1=5$
With the three points, $(2,-3), (0,1), (-2,5)$, we can graph the straight line that goes through these points.
The intersection point between these two lines is the answer to the system of equations.
In this case, the lines do not intersect, so the system of equations has no solution. This means that the lines are parallel.
