zMath 180  - Unit 30: Systems of Equations
Print out the figure below (right-click, Print Picture), and then graph the given equation using the slope-intercept method. Refer to the graph to answer the first six questions.

1) Point A is the:

2) Three-fourths is the:

3) Count up 3 to show the ________of the slope.

4) After counting up 3, then count 4 to the right to show the _________ of the slope.

5) Based on the previous two problems and the slope ratio, rise/run, plot point B. What are the coordinates of point B?

6) True or False. All points that fall on a line that passes through points A and B satisfy the equation, y = (3/4)x – 2.

7) The graph of a system of two equations is shown below. How many solutions does the system have?

8) The graph of a system of two equations is shown below. How many solutions does the system have?

9) The graph of a system of two equations is shown below. How many solutions does the system have?

10) What is the solution of the system of equations shown below?

11) Graph the system of equations. How many solutions exist for this system of equations?

12) Graph the system of equations. How many solutions exist for this system of equations?

For the next two problems use a graphing calculator, if one is available, to graph the systems of equations. Otherwise, graph the system of equations on graph paper.

Instructions for using a graphing calculator: In the [Y=] editor, set Y1 = to the first equation and Y2 = to the second equation. Press [GRAPH] and then [TRACE]. Use the right and left arrows to trace along the line of one of the graphs until the cursor lands on the point of intersection. The x-value and the y-value will be displayed at the bottom of the screen.

13) What is the solution to the system of equations? State the x-value and the y-value.

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14) What is the solution to the system of equations? State the x-value and the y-value.

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15) Solve this system of equations using SUBSTITUTION. State the x-value and the y-value.

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16) Solve this system of equations using SUBSTITUTION. State the x-value and the y-value.

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17) Apply the problem-solving technique of systems of equations to solve the following problem: The sum of two numbers is 50. The difference of the two numbers is 14. What are the two numbers?

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Review

18) Try various values for “x” and solve for “y” in the given equation. Does this equation vary directly or indirectly in terms of “x”?

19) Evaluate.

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20) Evaluate.

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For the next two problems, refer to the chart below to change each standard measure to metric measure or vice versa.

21) 12 inches (in) = __________ centimeters (cm)

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22) 500 grams (g) = __________ ounces (oz)

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Label answers correctly for the next four problems.

23) What is the perimeter of a square with a side length of 3.2 inches?

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24) What is the circumference of a circle with a radius of 1.2 centimeters? Express the answer in thousandths.

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25) What is the surface area of a square prism that measures 4 centimeters by 4 centimeters by 7 centimeters?

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26) What is the volume of the prism in the previous problem?

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27) Use the values listed in the table to determine if the function is linear or nonlinear.

28) Is the graph linear or nonlinear?

29) Graph the three equations, and then describe the change in the graphs as the number subtracted from x-squared increases in value.

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30) Graph the two equations, and then describe the change in location between the two graphs.

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31) Graph the two equations, and then describe the direction of the both graphs.

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32) What are the two roots of the quadratic equation?

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33) Graph the quadratic equation. What are the two roots of the equation?

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For the next two problems, consider the point X(5, 4) and Y(–3, –2) on the straight line XY.

34) What is the slope of line XY?

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35) What is the midpoint between point X and point Y?

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Consider triangle XYZ on a coordinate plane with points X(1, 1), Y(5, 1), and Z(3, 6). If necessary, draw triangle XYZ on graph paper to aid in answering the next six problems.

36) Translate triangle XYZ right 2 units, then up 3 units. What are the new coordinates of points X, Y, and Z?

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37) Translate the ORIGINAL triangle XYZ left 7 units, then up 4 units. What are the new coordinates of points X, Y, and Z?

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38) Rotate the ORIGINAL triangle XYZ 180 degrees about the origin, and then write the new coordinates of points X, Y, and Z.

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39) Rotate the ORIGINAL triangle XYZ 360 degrees about the origin, and then write the new coordinates of points X, Y, and Z.

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40) Reflect the ORIGINAL triangle XYZ over the x-axis, and then write the new coordinates of points X, Y, and Z.

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41) Reflect the ORIGINAL triangle XYZ over the y-axis, and then write the new coordinates of points X, Y, and Z.

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42) Apply the distributive property to simplify the expression.

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43) What is the sum of the interior angles of a hexagon?

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44) Collect the like terms to simplify the expression.

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45) Solve the equation for “x”.

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46) What is the solution to the given inequality? State the letter of the correct answer.

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