SAT -System of linear equations - chapter 2

Two lines that are graphed on the xy-plane intersect at the point (a, b). The first line has a slope of − 1/2 and passes through the point (−2, 2). The second line passes through the points (−1, −1) and (1, 3). What is the value of ab?

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

A nursery sells fertilizer in 25-pound and 100-pound bags. If Juliet bought 13 bags of fertilizer for her landscaping business that contained 775 pounds of fertilizer, how many 100-pound bags did she buy?

• 5

• 6

• 7

• 8

Tags

CCSS.8.EE.C.7B

Line l has a slope of 1 2 and an x-axis intercept of −4. Line m is perpendicular to line l. The two lines intersect on the y-axis. Which of the following is the equation of line m?

• y = -2x +2

• y = -2x + 4

If a is a constant for the given system of equations on the left, for what value of a will the system of equations have no solution?

• -7

• 2

• 4

• 14

Tags

CCSS.8.EE.C.8B

Due to train schedules, it takes Yvette longer to return from work to her home in the evening than it takes for her to get from home to work in the morning. If Yvette’s average total daily commuting time was 1 hour 12 minutes and her average morning commuting time was 8 minutes less than her evening average, what was her average commuting time returning home?

• 32 minutes

• 36 minutes

• 40 minutes

• 42 minutes

For which of the following values of m and b does the system of equations above have exactly two real solutions?

• m = −1, b = −6

• m = −1, b = 10

• m = 2, b = − 10

• m = 2, b = − 6

Tags

CCSS.HSA.REI.C.7

The 8 soup cans in Carlos’s pantry contain either 8 or 12 ounces each. Carlos has 4 ounces more soup in 8-ounce cans than in 12-ounce cans. How many 12-ounce cans of soup are in his pantry?

• 2

• 3

• 4

• 5

Tags

CCSS.8.EE.C.7B

The lines for the two equations on the left are parallel and separated by a vertical distance of 2 when graphed in the xy-plane. Which of the following could be the value of b?

• 2

• 3

• 4

• 6

Answer explanation

Parallel lines share the same slope but have a different y-intercept.

Since the separation of the two lines is 2, the constant term for the first equation must be 12 or 16.

Use these properties to solve for a and then b.