Question

Select the system of equations that corresponds to the given graph. (graph in comments)



4x + 2y = 12
4x + 2y = 4

2x + 3y = 4
6x + 9y = 12

2x + 4y = 12
2x + y = 3

2x + 3y = 8
−x + y = −4

Answer 1

from the graph u have that these two lines are prallel...two lines are parallel when they have the same slope
so at the first system u have 4x + 2y = 12 slop=-a/b=-4/2=-2
4x + 2y = 4 slope=-a/b=-4/2=-2
the slopes are the same

the second system 2x + 3y = 4 slope=-a/b=-2/3
6x + 9y = 12 slope=-a/b=-6/9=-2/3
the slopes are the same...

the other systems do not represent parallel lines so let's see which of the lines in which system has intercepts (0;2) (0;6) (1;0) (3;0)

the first system is 4x + 2y = 12 intercepts (0;6) (3;0)
4x + 2y = 4 intercepts (0;2) (1;0)
4x+2y=12 x-intercept,take y=0 and solve the equation for x,4x=12->x=12/4->x=3 (3:0)
y-intercept,take x=0 and solve for y,2y=12->y=12/2=6-> (0;6)
do the same with the second equation and you'll get (0;2) (1;0)
so this graph represents the first system