Solving a System of Equations Using Substitution Math 8

What does
"solution to a system of equations"
mean?

• It's the point where both equations equal zero
• It's the point where graphs of both equations cross the y-axis
• It's the point that solves both equations at the same time
• It's the point where graphs of both equations cross the x-axis

Tags

CCSS.8.EE.C.8B

How many solutions does this system have? And why?

• Infinitely many because they are parallel and never cross

• No solution because they are parallel and never cross

• One because math, and all lines cross sometime

• Can't tell without seeing the equations

What can you tell from just looking at these equations?

• They have different y-intercepts, so this system has 1 solution

• Both equations have a slope of 4, so this system has infinitely many solutions

• Both equations have a y, so they'll cancel each other out

• Both equations have the same slope, and different y-intercepts so they are parallel lines.

Solve this system of equations using substitution:

y = 3x + 3

y = -2x -2

• (-1, 0)

• (1, 0)

• (0, -1)

• (0, 1)

Solve this system using substitution:
3x + 4y = 15
y = 3

• (3, 1)
• (4, 3)
• (3, 4)
• (1, 3)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve this system of equations:
2x + 2y = 12
y = 2x

• (2, 2)
• (3, 6)
• (4, 2)
• (2, 4)

Jess correctly graphs a system of equations on her calculator but sees only one line as a result. What does this mean?

• The system has one solution
• The system has no solutions
• The system has infinite solutions
• The calculator's broken

Tags

CCSS.8.EE.C.8A

Which answer has a correct first step for this system:

3x + 3y = 3

y = 3x + 5

• The variable is already isolated, so we've already solved the system.

• The variable is already isolated for y, so we substitute it in the first equation and solve for x

  3x + 3(3x + 5) = 3

• Free sha vaca doo

• The variable is already isolated for y, so we substitute it in the second equation and solve for x

  y = 3(3x + 3y) = 3

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Which answer has a correct first step for this system:

3x + 3y = 3

y = 4

• One variable is already solved for a value, so we've already solved the system. Who cares what the value of x is?

• The variable is already solved for y, so we substitute it in the first equation and solve for x

  3x + 3(4) = 3

• I ain't get no sleep because y'all, y'all ain't get no sleep cuz of me

• The variable is already isolated for y, so we substitute it in the second equation and solve for x

  4 = 3x + 3y

Solve this system using substitution:

3x + 3y = 3

y = 0

• (1,0)

• (2,0)

• (-1,0)

• And they were roommates