The following problem was given on Keisha's Algebra 1 semester final.

Determine if (3,4) is a solution to the equation 2x + y = 10.

Keisha prefers to use the substitution method to solve this problem and would rather not solve this equation for y. What is the first step Keisha should take in solving this problem?

A. Keisha should solve the equation for y.
Incorrect. Please read the problem carefully. Keisha would rather not solve the equation for y.

B. Keisha should replace x and y with 3 and 4, respectively.
Correct! Keisha should substitute the given x and y coordinates into the equation.

C. Keisha should use the graphing calculator to review the graph of the equation.
Incorrect. Select the first step for solving by substitution.

D. Keisha should determine whether or not substituting the coordinates will yield a true statement.
Incorrect. Although this is the goal when solving by substitution, this is not the first step.

Joseph submitted the following solution to the problem below.

Determine a solution for the inequality 2y + 4x ≥ 6.

Joseph's Solution:

Above is the graph of the inequality 2y +4x ≥ 6. The inequality solved for y is y≥ -2x + 3. A solution to this inequality is (3,2).

What is the error in Joseph's solution?

A. Joseph incorrectly solved for y.
Incorrect. The inequality is correctly solved for y.

B. There is no error in Joseph’s solution.
Incorrect. Please review the graphing method for solving inequalities.

C. Joseph did not shade the correct portion of the graph.
Correct! The solutions for this inequality or located on and above the graph of the line.

D. The ordered pair is not a solution to the inequality.
Incorrect. The ordered pair is a solution to the inequality.

Luis is given the following problem to complete for homework.

Determine if (3,-8) is a solution to the equation -10x − 5y = 20

Luis prefers to use the table function on his graphing calculator to solve this problem. Which answer best represents a process Luis used to solve this problem?





A.
Correct! You must correctly solve the equation for y and input into the y = function before accessing the table function.

B.
Incorrect. Solve the equation for y before using the y = function.

C.
Incorrect. Solve the equation for y before using the y = function.

D.
Incorrect. This is not the correct graph for the equation. In addition, utilizing a graph is not Luis’ preferred method when solving this problem.

Arlette was given the following problem to complete for homework.

Determine if the point (9, 1.5) is a solution to the equation x − 2y = 6.

Arlette prefers to find the solution by graphing the equation on the graphing calculator and utilizing the table function. Her solution is below.

A.There is no error in Arlette’s solution.
Incorrect. Please review the tabular method for solving equations.

B. The table function cannot be used to solve this problem.
Incorrect. Please review the tabular method for solving equations.

C. Arlette should have used the trace function on the graphing calculator to determine if the point lies on the graphed the line.
Incorrect. Although the trace function may be used to solve the problem, Arlette prefers to use the table function.

D. The equation is incorrectly solved for y.
Correct! The equation is incorrectly solved for y. The correct equation is y = x/2 – 3.