Solving Linear Systems Graphically Assignment 2

Solve the system.2x + y = −3 −2y = 6 + 4x Write each equation in slope-intercept form.

-2 -3 -2 -3

Solve the system.2x + y = 3 −2y = 14 − 6x Write each equation in slope-intercept form.

-2 3 3 -7

How do the slopes and y-intercepts of the two equations compare?

....

what do the equations have in common?

The two equations are identical, so there are an infinite number of solutions. For any choice of x, the value of y is -2x-3.

Explain how you can determine that the following system has one unique solution - without actually solving the system.

To do so, get every part into slope-intercept form (y = mx + b).If the slopes are different, there is one solution.If the slopes the same but the y intercepts different, there is no solution.If the slopes and y intercepts are the same, there are infinitely many solutions.

The system represents lines that _____ there for the system

are parallel no solution

the system represents lines that there fore the system has

intersect at one point exactly one solution

What do the equations have in common? How are they different?

same slope different y intercepts

Analyze the solution set of the following system by following the given steps.2x + y = 5 3y = 9 − 6x Write each equation in slope-intercept form.

-2 5 -2 3

Consider the system:y = 3x + 5y = ax + bWhat values for a and b make the system inconsistent? What values for a and b make the system consistent and dependent? Explain

When a = 3 and b ≠ 5, the system will be inconsistent because the lines will be parallel. When a = 3 and b = 5, the system will be consistent and dependent because they represent the same line

How should you modify the graph to show the solution to the system of inequalities below? Check all that apply. Shade above 2x + y = 4. Shade below 2x + y = 4. Shade above 2y = 6 - 2x. Shade below 2y = 6 - 2x. Make the boundary line 2x + y = 4 dashed.

a. shade above 2x + y = 4 d. shade below 2y = 6 - 2x e. make the boundary line 2x + y = 4 dashed

The system represents lines therefore the system has

coincide infinitely many solutions