Linear Equations and Systems of Linear Equations

Solve the system of linear equations by graphing.

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The equations of two lines are 6x + y = 26 and y = 2x + 10. If the solution is (2, y), what is the value of y?

• 14

• 4

• 6

• 2

Define two variables, write a system of equations, then solve. Sue plans to mix peppermints worth $1.20 per lb with chocolates worth $2.40 per lb to get a 40 lb mix that is worth $1.65 per lb. How much of each should she use?

• 25 lbs peppermints, 15 lbs chocolates

• 20 lbs peppermints, 20 lbs chocolates

• 15 lbs peppermints, 25 lbs chocolates

• 30 lbs peppermints, 10 lbs chocolates

-6x+5y=1
6x+4y=-10

• (1,-1)

• (0,-1)

• (1,1)

• (-1,-1)

What is the value of x in the following system of equations:

2x - y = 4

y = -2x + 8

• 8

• 11

• 3

• 5

Here is the graph for one of the equations in a system of two equations. The solution to the system is (0, -2). Select the equation that could be the other equation in the system.

• y = -2x + 1

• y = - 1/4x + 2

• y = x - 1

• y = - 3/2x-2

Which of the following linear functions is parallel to the function graphed below?

• y = -1/2 x  + 3

• y = 2x + 1

• y = - x  + 1

• y = - 2x + 3

This system has _____ solutions

• no

• 1

• 2

• Infinitely many

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38
  2s + 3c = 52

• 3s + 1c = 38
  3s + 2c = 52

• s + c = 38
  s + c = 52

• 3s + 3c = 38
  1s + 2c = 52

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? 

• x + y = 1550
  y  = 4x

• x + y = 1550
  y = x + 4

• y - x = 1550
  y = 4x

• y = 1550 + x
  y = x + 4