Question

topic: graphing systems of linear equations
progress
match each system on the left with all words that describe the system on the right. choices on the right can be used more than once.

1. $y = 2x + 3$

$x + y = -3$

1. $3y = 9x - 6$

$3y - 6x = 4$

1. $y = -\frac{1}{2}x + 2$

$x + 2y = 4$

descriptions:
inconsistent
consistent
independent
dependent

click and hold an item in one column, then drag it to the matching item in the other column. be sure your cursor is over the target before releasing. the target will highlight or the cursor will change. need help? watch this video.
clear

Explanation:

Step1: Analyze first system

System: $y=2x+3$, $x+y=-3$
Substitute $y=2x+3$ into $x+y=-3$:
$x + (2x+3) = -3$
$3x + 3 = -3$
$3x = -6$
$x = -2$, $y=2(-2)+3=-1$
One unique solution → consistent.

Step2: Analyze second system

System: $3y=9x-6$, $3y-6x=4$
Simplify first equation: $y=3x-2$
Substitute into second equation:
$3(3x-2)-6x=4$
$9x-6-6x=4$
$3x=10$
$x=\frac{10}{3}$, $y=3(\frac{10}{3})-2=8$
One unique solution → consistent.

Step3: Analyze third system

System: $y=-\frac{1}{2}x+2$, $x+2y=4$
Substitute $y=-\frac{1}{2}x+2$ into $x+2y=4$:
$x + 2(-\frac{1}{2}x+2)=4$
$x -x +4=4$
$4=4$
Infinite solutions → dependent.

Answer:

• $y=2x+3$ and $x+y=-3$ → consistent
• $3y=9x-6$ and $3y-6x=4$ → consistent
• $y=-\frac{1}{2}x+2$ and $x+2y=4$ → dependent

(Note: The "inconsistent" and "independent" labels have no matching systems here, as inconsistent systems have no solutions, and independent refers to non-dependent consistent systems, which both first two systems are, but the only non-dependent consistent option provided is "consistent".)