Solving Systems by Graphing (HIKE)

Solve the system by graphing: 3x + y = -1 2x + y = 0

(-1, 2)

Solve the system by graphing: y = 6 2x + 3y = 12

(-3, 6)

Solve by graphing -2x = -y + 1 -4x + y = -1

(1, 3)

Solve by graphing -x + y = 1 3x + 2y = 12

(2,3)

Solve the system by graphing: -x + y = 1 2x + y = 10

(3, 4)

Solve by graphing: x - 3y = -3 x + y = 5

(3,2)

Solve the system by graphing: 2x + y = 7 x - 2y = 6

(4, -1)

Solve the system by graphing: 2x + y = 6 x + y = 1

(5, -4)

Fill in the blank. If two lines have different slopes (m) they are __________lines.

If two lines have different slopes (m) they are INTERSECTING lines.

Fill in the blank. If two lines have same slopes (m) AND same y-intercepts, they are __________lines.

If two lines have same slopes (m) AND same y-intercepts, they are COINCIDENT lines (this means they will be the same! Infinitely many solutions).

Fill in the blank. If two lines have the same slope (m), but different y-intercepts (b), they are __________lines.

If two lines have the same slope (m), but different y-intercepts (b), they are PARALLEL lines.

Solve the system by graphing: y = -3x - 6 6x + 2y = -12

Infinitely many solutions (since the lines are the same, every point on the line makes both equations true. There are infinite solutions).

Solve the system by graphing: y = 1/2x - 4 2x - 4y = 16

Infinitely many solutions (since the lines are the same, every point on the line makes both equations true. There are infinite solutions).

Solve the system by graphing: y = 2x - 3 -6x + 3y = -9

Infinitely many solutions (since the lines are the same, every point on the line makes both equations true. There are infinite solutions).

A system has no solution if what is true?

The lines are parallel

Solve the system by graphing: 2y = x - 6 x - 2y = 4

no solution (since the lines are parallel, there is no solution to this system)

Solve the system by graphing: y = -1/4 x + 2 x + 4y = -8

no solution (since the lines are parallel, there is no solution to this system)

Solve the system by graphing: y = 3x - 1 6x - 2y = 6

no solution (since the lines are parallel, there is no solution to this system)

Write the following system in slope intercept form. 2x + y = 7 x - 2y = 6

y = -2x + 7 y = 1/2x - 3

Write the following system in slope intercept form. 3x + y = -1 2x + y = 0

y = -3x - 1 y = -2x

Write the following system in slope intercept form. x - 3y = -3 x + y = 5

y = 1/3x + 1 y = -x + 5

Write the following system in slope intercept form. -2x = -y + 1 -4x + y = -1

y = 2x + 1 y = 4x - 1

Write the following system in slope intercept form. -x + y = 1 3x + 2y = 12

y = x + 1 y = -3/2x + 6