Adv Math: System of equations with two variables

inconsistent

consistent

dependent

independent

dependent

consistent

independent

inconsistent

three linear equations with the same variables

two or more linear equations with the same variables

two or more linear equations with different variables

one linear equations with one variable

one solution

two solutions

infinitely many solutions.

has no solution

Consistent

inconsistent

dependent

independent

The lines are not in slope-intercept form (y=mx+b)

The lines have the same slope and y-intercept

The lines are perpendicular

The lines are parallel

 $\left(\frac{2}{3},-\frac{1}{3}\right)$  

 $\left(\frac{1}{3},\frac{2}{3}\right)$  

 $\left(-\frac{2}{3},\frac{1}{3}\right)$  

 $\left(-\frac{1}{3},-\frac{2}{3}\right)$  

$y=3x+4$
$-12x+4y=16$

$x+2y=10$
$2x+4y=10$

$y=2x+6$
$4x-2y=8$

d + c = 174

4d + 2c = 50

d + c = 50

4d + 2c = 174

d + c = 50

2d + 4c = 174

d + c = 174

2d + 4c = 50