Look at the system of linear equations graphed on the coordinate grid.

Which of the following is closest to the solution to this system of linear equations?

A.
Incorrect. The point is graphed above the lines and is not the intersection.

B.
Incorrect. The point is not the intersection.

C.
Correct! The x-value is between -6 and -7. The y-value is between 1 and 2.

D.
Incorrect. The point is graphed below the lines and is not the intersection.

The following graph represents a system of equations. What appears to be the number of solutions to this system of equations?

A. 0
Correct! The lines are parallel so there in no intersection and no solution.

B. 1
Incorrect. The lines are parallel not intersecting.

C. 2
Incorrect. There cannot be two intersection points with a system of linear equations.

D. Infinite
Incorrect. The lines are parallel not coinciding.

2x + 3y = 8

x − 2y = -7

Which graph best represents a solution to this system of equations?

A

B

C

D

A.
Incorrect. The lines should intersect in the second quadrant.

B.
Incorrect. The graph of the lines should look like this.

C.
Incorrect. The graph of the lines on the calculator intersect in the 2nd quadrant.

D.
Correct! The graph on the calculator matches this one.

What is the x-coordinate of the solution to the system of linear equations below?  

4x + 5y = 8
2x − 3y = -18

A. -4
Incorrect. Using TRACE and keying in -4 does not give the intersection.

B. -3
Correct! (-3, 4) is the intersection so -3 is the x-coordinate.

C. 3
Incorrect. Using TRACE and keying in 3 does not give the intersection.

D. 4
Incorrect. Using TRACE and keying in 4 does not give the intersection.

At a toy store the total cost of 5 X-Men action figures and 2 Yes Man action figures is $42.75, including tax. The total cost of 10 X-Men action figures and 3 Yes Man action figures is $82.25, including tax. What is the cost for each Yes Man action figure?

A. $3.25
Correct! The y-value is 3.25 and the x-value is 7.25.

B. $7.25
Incorrect. If you write the two equations and change them to slope-intercept form you can use a graphing calculator. Use trace and notice that the point of intersection is somewhere between 7 and 8 and then you want to find the y-value at that point which is between 3 and 4. The only answer possible is A.

C. $6.50
Incorrect. If you change them to slope-intercept form you can use a graphing calculator. You can find the intersection using the CALC on the calculator, above TRACE. The y-value is 3.25.

D. $16.25
Incorrect. If you write the two equations and change them to slope-intercept form you can use a graphing calculator. You can use TRACE to find the point of intersection or use CALC on the calculator to find the intersection The y-value is 3.25.