LHS A2 Unit 3 Systems + inequalities

Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-3,-8)

• (-8,-3)

• (3,-8)

• (8,3)

Answer explanation

The solution to the system of equations is the point where the two lines intersect. In this case, the correct intersection point is (-3,-8), which satisfies both equations.

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Each table represents (x,y) coordinates from two different equations of lines.

The two lines are part of a system of equations.

What is the solution of the system of equations?

• (5, 11)

• (2, 5)

• (-1, 1)

• (11, 5)

Answer explanation

The solution of the system of equations is the point where the two lines intersect. The coordinates (5, 11) satisfy both equations, making it the correct answer.

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Answer explanation

To check which point lies on the graph of y = 2x + 3, substitute the x-value into the equation. For (0, 3): y = 2(0) + 3 = 3. This is correct. The other points do not satisfy the equation.

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.CED.A.2

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

Answer explanation

Substituting y = 2x + 1 into 3x + y = 11 gives 3x + (2x + 1) = 11. Simplifying, we get 5x + 1 = 11, leading to 5x = 10, so x = 2. Substituting x back, y = 2(2) + 1 = 5. Thus, the solution is (2, 5).

Tags

CCSS.HSA.REI.C.6

Answer explanation

To solve the system using elimination, multiply the first equation by 2: 4x + 6y = 12. Now, subtract the second equation: (4x + 6y) - (4x - 3y) = 12 - 12, leading to 9y = 0, so y = 0. Substitute y back to find x = 3. Thus, the solution is (3, 0).

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.5

Answer explanation

To solve the system, substitute y from the first equation into the second: x - (5 - x) = 1. This simplifies to 2x - 5 = 1, giving x = 3. Substituting x back, y = 2. Thus, the solution is (3, 2).

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.5

Answer explanation

To check if a point is in the solution set of the inequality y < 2x + 1, substitute the coordinates into the inequality. For (0, 0): 0 < 2(0) + 1 is true. For others, they do not satisfy the inequality. Thus, (0, 0) is correct.

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

• Above both lines

• Below both lines

• Between the lines

• No solution

Answer explanation

To solve the inequalities, graph the lines. The first inequality, y ≥ x - 2, includes the area above the line, while the second, y < -x + 4, includes the area below the line. The solution set is the region between the two lines.

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

Answer explanation

To solve the system, substitute y from the first equation into the second: y = 10 - 2x. Then, x - (10 - 2x) = 1 leads to 3x = 11, so x = 4. Substituting x back gives y = 2. Thus, the solution is (4, 2).

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.5

Answer explanation

To check which point lies on the line defined by 3x - 2y = 6, substitute each point into the equation. (2, 0) gives 3(2) - 2(0) = 6, which is true. (0,-3) works as well. 3(0)-2(-3) = 6

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.CED.A.2