Linear Equations Challenge

Solve the system of equations: 2x + 3y = 6 and x - y = 2. What are the values of x and y?

• x = 0, y = 2

• x = 12/5, y = 2/5

• x = 3, y = 0

• x = 1, y = 1

Graph the equations y = 2x + 1 and y = -x + 4 on the same coordinate plane. What do you observe about their slopes?

• The slopes are equal and both are negative.

• One slope is zero and the other is positive.

• The slopes of the lines are different; one is positive (2) and the other is negative (-1).

• Both slopes are positive.

Identify whether the lines represented by the equations 3x + 2y = 12 and 6x + 4y = 24 are parallel, intersecting, or coincident. Explain your reasoning.

• none of the above

• intersecting

• coincident

• parallel

Determine the intersection point of the lines given by the equations y = 3x - 5 and y = -2x + 4. What is the point of intersection?

• (9/5, 2/5)

• (2, 3)

• (0, 0)

• (1, -1)

If the equations 4x - y = 8 and 4x + 2y = 16 are graphed, will they intersect? If so, find the intersection point; if not, explain why.

• The equations do not intersect because they are parallel.

• The equations intersect at the point (0, 8).

• The equations intersect at the point (8/3, 8/3).

• The equations intersect at the point (4, 0).