Write Systems of Linear Equations, (Tables & Graphs), TEKS A.2I

Write Systems of
Linear Equations

Tables & Graphs

A set of 2 or more equations with the same variables.

System of Equations:

Steps to Writing Systems of Equations:

1.) Find the slope (m) and y-intercept (b) of each graph or table.

2.) Write the equation in Slope-Intercept form (y = mx + b).

3.) Convert to Standard Form (AX + BY = C), if necessary.

Writing Systems of Equations from Tables:

1.) Do a Linear Regression to find m (slope) and b (y-intercept).

2.) Write in Slope-Intercept form (y = mx + b).

3.) Convert to Standard form (AX + BY = C), if necessary.

Linear Regression Steps:

1.) Go to the Home Screen and create a New Document. Answer No to the save question.
2.) Press 4 for Add Lists & Spreadsheets.
3.) Scroll up to the A column and type x; Then type y in the B column.
4.) Type your points in the table.
5.) Press Menu/4-Statistics/1-Stat Calculations/3-Linear Regression, mx+b
6.) Double click under the X-list to select x; then click on the Y-list to select y.
7.) Press Enter. The calculator will tell you the m (slope) and b (y-intercept).

Multiple Choice

Convert the following equation from standard form to slope-intercept form: 4x + 2y = 14

• y = 4x + 14

• y = -2x + 14

• y = -2x - 14

• y = -2x + 7

Multiple Choice

Convert the following equation from standard form to slope-intercept form: -9x + 3y = -12

• y = -3x - 4

• y = -3x + 4

• y = 3x + 4

• y = 3x - 4

Multiple Choice

The tables give the costs of renting a bike from two different bike shops. The total charge, y, is a linear function of the number of hours a bike is rented, x, plus a service charge.

Which system of equations represents the situation?

• $$y=12x+12$$ and $$y=10x+6$$

• $$y=12x+12$$ and $$y=12x+2$$

• $$y=8x+16$$ and $$y=10x+6$$

• $$y=8x+16$$ and $$y=12x+2$$

Multiple Choice

Casey works two part-time jobs. She earns $9 per hour as a stockroom clerk and $12 per hour as a cashier, a total of $288 weekly. The graph shows the relationship between the number of hours she works at each job each week. The table models the amount of time she must work at each job to make $288.

Which system of equations represents the graph and the table?

• $$x+y=27$$ and $$9x+12y=288$$

• $$x+y=27$$ and $$x+y=288$$

• $$x-y=27$$ and $$12x+9y=288$$

• $$x-y=27$$ and $$x+y=288$$

Multiple Choice

Two graphs are shown below. What is the system of equations represented by the graphs?

• $$y=-\frac{1}{2}x-2$$ and $$y=x+1$$

• $$y=-\frac{1}{2}x-2$$ and $$y=-x+1$$

• $$y=2x-2$$ and $$y=x+1$$

• $$y=-2x-2$$ and $$y=x+1$$

Multiple Choice

An athlete is in training for a triathlon. One day the athlete covered 27 miles, running for 2 hours and riding a bike for 1 hour. Another day the athlete ran and biked at the same speeds as before, but covered a different total distance. The table models the linear relationship between x, the running speed, and y, the biking speed, the second day for second day for several possible speeds over that distance. What system of equations represents the two training sessions?

• $$2x+y=27$$ and $$x+y=18$$

• $$x+y=27$$ and $$\frac{1}{2}x+y=18$$

• $$2x+y=27$$ and $$\frac{1}{2}x+y=18$$

• $$x+y=27$$ and $$2x+y=18$$

Multiple Choice

Each day, a worker earns $15 per hour and spends $23 on food and transportation. The graph models a different worker’s earnings after paying for food and transportation.

Which system of equations represents the total earnings y of the workers after x hours of work?

• $$y=15x+23$$ and $$y=12x+8$$

• $$y=15x-23$$ and $$y=12x-8$$

• $$y=x-23$$ and $$y=x-8$$

• $$y=15x-23$$ and $$y=x-8$$

Multiple Choice

Ordered pairs for two linear equations are listed in the tables below.

Which system of equations, when solved, could be used to find the ordered pair that satisfies both equations?

• $$y=-2x+2$$ and $$y=x-2$$

• $$y=-3x+6$$ and $$y=x-2$$

• $$y=x+6$$ and $$y=x-2$$

• $$y=3x+6$$ and $$y=2x-5$$

Multiple Choice

The first graph below represents the altitude of Plane 1 as it descends to an airport. The second graph represents the altitude of Plane 2 as it ascends from an altitude of 1,000 feet. Let x represent the plane’s altitude, in feet, and let y represent the length of time the plane has been flying, in minutes.

Which system of equations, when solved, will give the time when the planes are at the same altitude?

• $$y=500x+10,000$$ and $$y=40x+1,000$$

• $$y=-500x+10,000$$ and $$y=400x-1,000$$

• $$y=-500x+10,000$$ and $$y=400x+1,000$$

• $$y=-x+10,000$$ and $$y=400x+1,000$$

Multiple Choice

A freight train traveled 510 miles, part of the time at an average speed of 50 mi/h, the rest at an average speed of 60 mi/h. The table models the linear relationship between x, the length of time traveling 50 mi/h, and y, the length of the time traveling 60 mi/h.

Which system of equations can be solved to find the length of time the train traveled at each speed?

• $$x-y=9$$ and $$50x+60y=510$$

• $$x+y=9$$ and $$50x+60y=510$$

• $$x+y=9$$ and $$60x+50y=510$$

• $$x+y=510$$ and $$50x+60y=9$$

Multiple Choice

Two graphs are shown below. What is the system of equations represented by the graphs?

• $$y=2x+2$$ and $$y=x+1$$

• $$y=\frac{1}{2}x+2$$ and $$y=-x+1$$

• $$y=\frac{1}{2}x+2$$ and $$y=x+1$$

• $$y=2x+2$$ and $$y=-x+1$$

Multiple Choice

The graph represents the possible numbers of nickels and dimes in a student’s coin jar if the student has 16 coins in all. The coordinate pairs in the table represent some possible combinations of nickels and dimes that are worth $1.60.

Which system of equations represents the situation? 

• $$x+y=16$$ and $$5x+10y=160$$

• $$x-y=16$$ and $$x+y=160$$

• $$x+y=16$$ and $$x+y=160$$

• $$x-y=16$$ and $$5x+10y=160$$

Poll

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