Solutions Algebra

Two equations are given.

y=3x and y=x+1

What values of y and x will satisfy both equations?

• y=1.5, x = 0.5

• y=3, x =1

• y=0.5, x=1.5

• y=1, x = 0

Two equations are given.

y= -8x+56

2x+2y=56

Which ordered pair will satisfy both equations?

• (-4, -24)

• (-2, -12)

• (2, 12)

• (4, 24)

A system of equations is shown.

2x + 5y = 16

x - 8y = -13

What is the x-value of the solution to the system of equations?

• 1

• 2

• 3

• 4

What is the x-value which makes the system of equations true?

2x - 3y = 12

x + y = -4

• -24

• -4

• 0

• 2

Study the system of equations.

x + y = 9

2x - y = 6

What is the y-value for the point of intersection in this system of equations?

• 4

• 5

• 9

• The lines do not intersect

In a football game, Sebastian scored points by kicking the football through the goal posts successfully 9 times. Each of the successful kicks was worth either 1 point (an extra point after a touchdown) or 3 points (a field goal). Sebastian scored a total of 17 points as the kicker.

If x represents the number of 1-point extra points, and y represents the number of 3-point field goals, which system of equations should be used to model the situation?

• 1x + 3y = 9

  x + y = 17

• 1x + 3y = 17

  x + y = 9

• 3x + 1y = 9

  x + y = 17

• 3x + 1y = 17

  x + y = 9

Study the system of equations in the box.

2x + y = 10

3x + 15y = -12

What is the point of intersection for the system of equations?

• (0.07, 0.79)

• (1.27, 0.04)

• (5, 0)

• (6, −2)

Fredrick wrote a system of equations that has the same solution as the system of equations in the box.

2x + 3y = 8

4x - y = 2

Which systems of equations did Fredrick write?

• 6x+4y=10

  2x+3y=8

• 6x+2y=10

  7y=14

• 2x+3y=8

  14x=10

• 2x+3y=8

  10x+y=10

JoLisa is playing a matching game involving systems of equations. Four different systems are shown. If JoLisa picks two sets of systems which have the same solution, she will win the game.

A: 2x+6y=12 and 4x + 8y =20

B: 4x+12y=24 and 6x+14y+32

C: 8x + 16y = 20 and 2x + 2y = 8

D: 6x + 14y = 32 and 8x + 24y = 12

Which 2 systems of equations should JoLisa pick to win the game?

• A and B

• B and C

• C and D

• D and A

A system of linear equations is given.

3x + 7y = 10

x + y = 2

Which system of linear equations will have the same solution as that of the given system of linear equations?

• 3x+7y=10

  2x+2y=4

• 3x+7y=10

  4x+8y=2

• 6x+14y=10

  x+y=2

• 4x+8y=10

  x+y=2