EOC Bootcamp Day 4 - Systems of Linear Equations

Systems of Linear Equations

Using DESMOS to graph

Solution to System is the intersection point

• Make sure Y or X is completely isolated

• Plug equations into Desmos

• Solution to a system

  • Look for the intersection point - click on it

  • ANSWER the question​

Use Desmos to graph the two lines

Multiple Choice

A system of equations is graphed on the grid.

Which system of equations does the graph represent?

• $$y=-x-4$$

  $$y=2x-2$$

• $$y=-x+4$$

  $$y=2x-4$$

• $$y=x-4$$

  $$y=-2x-2$$

• $$y=x+4$$

  $$y=-2x-4$$

Multiple Choice

The graph shows a system of linear equations. Which of the following could be used to determine the solution?

• 3x − 2y = 8

  7x + 4y = −28

• 3x + 2y = −8

  7x − 4y = 28

• 3x + 2y = 8

  7x − 4y = −28

• 3x − 4y = 28

  7x + 2y = −8

Multiple Choice

What is the value of y in the solution to this system of equations?

$$6y+x=-59$$

$$x=-2y+9$$

• 8.5

• -17

• 43

• -12.5

Multiple Choice

The tables of ordered pairs represent some points on the graphs of f and g.

Which system of equations represents lines f and g?

• $$y=1.75x+3.5$$

  $$y=-4x-8$$

• $$y=1.75x+3.5$$

  $$y=-4x-2$$

• $$y=3.5x+1.75$$

  $$y=-4x-8$$

• $$y=3.5x+1.75$$

  $$y=-4x-2$$

Multiple Choice

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same.

Which system of equations can be used to find the price in dollas of each large candle, x, and each small candle, y?

• $$4y=3x+64$$

  $$8y=x+68$$

• $$4y=3x+64$$

  $$8y=x+60$$

• $$3x+4y=64$$

  $$x+8y=68$$

• $$3x+4y=64$$

  $$x+8y=60$$

Multiple Choice

A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses.

How many courses worth 3 credits did the student complete?

• 13

• 5

• 20

• 39

Solving One-Variable Equations in Desmos

• Change variable to x

• Type the left side into Desmos

• Type the right side into Desmos

• Look for the intersection point, click

• The X-VALUE IS THE ANSWER

Math Response

What is the solution to this equation?

$$2\left(40-5y\right)=10y+5\left(1-y\right)$$

Enter ONLY the numerical answer.

Type answer here

Correct Answer: 5

Deg^°

Rad

Multiple Choice

What value of x makes the equation $$-5x-\left(-7-4x\right)=-2\left(3x-4\right)$$ true?

• $$x=3$$

• $$x=5$$

• $$x=\frac{1}{3}$$

• $$x=\frac{1}{5}$$

Multiple Choice

Which value of x makes the equation $$0.75\left(x+20\right)=2+0.5\left(x-2\right)$$ true?

• 64

• -64

• 56

• -56

Multiple Choice

A bus travels two different routes: the Green Route and the Blue Routh. The routes are different lengths.

- On Monday the bus traveled the Green Route 6 times and the Blue Route 5 times, traveling a total of 52 miles.

- On Tuesday the bus traveled the Green Route 12 times and the Blue Route 13 times, traveling a total of 119 miles.

What is the length of the Green Route in miles?

• 4.4 mi

• 4.5 mi

• 6.4 mi

• 6.8 mi

Math Response

A manager purchased a total of 21 coffee mugs and key chains. Each coffee mug cost $8.50, and each key chain cost $2.75. If the manager spent a total of $132.50, how many coffee mugs did the manager purchase?

Enter ONLY the numerical answer.

Type answer here

Correct Answer: 13

Deg^°

Rad

Multiple Choice

A customer paid a total of $6.00 for 68 copies at a print shop. Some of the copies were black-and-white copies, and the rest were color copies.

- Each black-and-white copy cost $0.08

- Each color copy cost $0.15

Which system of equations can be used to find b, the number of black-and-white copies, and c, the number of color copies that the customer paid for at the print shop?

• $$b+c=6.00$$

  $$0.08b+0.15c=68$$

• $$b+c=68$$

  $$0.15b+0.08c=6.00$$

• $$b+c=6.00$$

  $$0.15b+0.08c=68$$

• $$b+c=68$$

  $$0.08b+0.15c=6.00$$

Multiple Choice

A system of linear equations is represented by line h and line j. A table representing some points on line h and the graph of line j are shown.

Which system of equations is best represented by lines h and j?

• $$y=\frac{4}{3}x-5$$

  $$y=\frac{4}{5}x+1$$

• $$y=\frac{3}{4}x-5$$

  $$y=\frac{5}{4}x+1$$

• $$y=-\frac{4}{3}x-5$$

  $$y=-\frac{4}{5}x+1$$

• $$y=-\frac{3}{4}x-5$$

  $$y=-\frac{5}{4}x+1$$

Multiple Choice

What is the solution to this system of equations?

$$2x+y=40$$

$$x-2y=-20$$

• (12, 16)

• (15, 17.5)

• There is no solution.

• There are an infinite number of solutions.

Multiple Choice

What is the value of x in the solution to this system of equations?

$$3x-5y=22$$

$$y=-5x+32$$

• -6.5

• 0.5

• 6.5

• -0.5

Multiple Choice

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

$$x=2y-4$$

$$7x+5y=-66$$

• -2

• $$-\frac{19}{7}$$

• -8

• $$-\frac{62}{19}$$

Multiple Choice

What is the value of x in the solution to this system of equations?

$$y+2x=-1$$

$$y=\frac{1}{2}x+4$$

• $$\frac{6}{5}$$

• -2

• $$-\frac{10}{3}$$

• 3

Multiple Choice

What is the solution to this system of equations?

$$10x-y=53$$

$$y=\frac{-13x+92}{2}$$

• (6, 7)

• (2, 33)

• (7, 6)

• (33, 2)