Mastering Linear Equations

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

• (3, 0)

• (0, 2)

• (1, 1)

• (12/5, 2/5)

Graph the equations: y = 2x + 1 and y = -x + 4. What do you observe?

• The intersection point is (2, 5).

• The lines are parallel and do not intersect.

• The two lines intersect at the point (1, 3).

• The two lines are identical.

Determine if the lines represented by 3x + 4y = 12 and 6x + 8y = 24 are parallel. Explain your reasoning.

• The lines are identical and overlap.

• The lines are perpendicular to each other.

• Yes, the lines are parallel.

• No, the lines intersect at a point.

Find the intersection point of the equations: x + 2y = 5 and 3x - y = 4.

• (0, 5)

• (2, 1)

• (1, 2)

• (13/7, 11/14)

Convert the equation 4x - 2y = 8 into standard form.

• 4x - 2y = 0

• 2x - y = 4

• 4x - 2y - 8 = 0

• 4x + 2y = 8

Solve the following equations: 5x + 2y = 10 and 3x - 4y = -2.

• x = 18/13, y = 20/13

• x = 1, y = 3

• x = 0, y = 5

• x = 2, y = 0

Graph the equations: y = 1/2x - 3 and y = 1/2x + 1. Are they parallel?

• No, they intersect at one point.

• Yes, they are the same line.

• Yes, they are parallel.

• No, they have different slopes.

Find the intersection point of the lines: 2x + y = 10 and x - 2y = -1.

• (3, 4)

• (10, 0)

• (5, 0)

• (19/5, 12/5)

Convert the equation y - 3 = 2(x + 1) into standard form.

• 3x + y = 6

• 2x + y = 1

• -2x + y = 5

• x - y = 3

Determine if the lines represented by x + 2y = 4 and 2x + 4y = 8 are parallel or coincident.

• coincident

• parallel

• intersecting

• perpendicular