Solve systems of equations and inequalities Review

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

• 3x + 2y = 315

  2x + 4y = 450

• 3x + 2y = 450

  2x + 4y = 315

• 2x + 2y = 315

  3x + 4y = 450

• 5x + 6y = 765

Which point is a solution?

• (0, 6)

• (-3, 4)

• (1, 1)

• (-4, 3)

What is the solution?

• (3, 6)

• (6, 3)

• (-6, 3)

• No solution

Are the points on the boundary line part of the solution set or not?

• Yes, they are part of the solution set

• No, they are NOT part of the solution set

• It is impossible to determine.

Which would be correct describing the solution for this graph of two inequalities?

• Any point that is NOT in the pink or blue is a solution to this system.
• Any point that falls in either the pink or blue is a solution to the system.
• Only a point that is on either boundary line is a solution to this system.
• There is no point that is a solution to this system.

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.12

Which points are solutions to the system shown?

• (5, 3) (6, -3)
• (3, 3) (5, -3)
• (-2, 2) (-4, 4)
• (1, 2) (1, 5)

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

What are systems of linear equations?

• a set of two or more linear equations in the same variables

• a polynomial with three terms

• set of two or more linear inequalities in the same variables

• an equation with one solution

If you are solving the system by elimination, one of the “best” strategies to accomplish this would be:

• Multiply the bottom equation by -2, and then subtract the two equations.

• Solve the bottom equation for y, and then substitute for y in the top equation.

• Multiply the top equation by -4, and then add the two equations together.

• Multiply the top equation by 8, and then multiply the bottom equation by 2. Then, add the two equations together.

How many solutions does this system of equations have?

• One Solution

• No Solution

• Two Solutions

• Infinitely Many Solutions

3x + 2y = 16

7x + y = 19

If you are solving the system of equations above by substitution, one of the “easiest” ways to do this would be:

• to solve the top equation for x, and then substitute into the bottom equation for x.

• to solve the bottom equation for y, and then substitute into the top equation for y.

• to multiply the bottom equation by -2 and add the two equations together.

• to set the two equations equal to each other and solve for x.