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# 13 Algebra Problems : Inequalities, Systems of Equations and Word Problems

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1.) Graph the inequality on a plane.
3x + 4y &#8804; 12

2.) Determine whether the ordered pair is a solution of the inequality.
(4, 13); 5y - 6x > 4
Is the ordered pair a solution? Yes or No

3.) Miguel's insurance company will replace his car if repair costs exceed 80% of the car's value. The car recently sustained \$9600 worth of damage, but it was not replaced. What was the value of his car?
4.) Solve by the substitution method.
2m + n =2
M - 9n =77
What is the solution of the system? (Type an ordered pair. Type N if there is no solution.)
5.) The perimeter of a rectangle is 96 m. The length is 3 m. Find the dimensions.
6.) Solve.
6(r - 7) + 2 > 7(r + 2) - 24
The solution set is {r|r __ __}. (Type an inequality symbol, then type an integer or a fraction.)
7.) A cellular phone company offers a contract for which the cost C, in dollars, of t minutes of telephoning is given by C=0.25(t - 300) + 67.95, where it is assumed that t &#8805; 300 minutes. What times will keep costs between \$112.45 and \$131.95?
For the cost to be between \$112.45 and \$131.95, the telephoning time must be between __ minutes and __ minutes.
8.) Solve the system by the elimination method.
5x + 5y = -11
7x - 2y = 17
What is the solution of the system? (Type an ordered pair. Type an integer or a fraction. Type N if there is no solution. Type I if there are infinitely many solutions.)
9.) Solve.
9/10(3 + 8x) + 3 &#8805; 15
The solution is {x|x__ __}. (simplify your answer. Type an inequality symbol; then type an integer or a fraction.)
10.) Solve by the elimination method.
0.3x - 0.2y = 4
0.2x + 0.3y = 5/23
What is the solution of the system? ____(Type an ordered pair. Type an integer or a fraction. Type N if there is no solution. Type I if there are infinitely many solutions.)
11.) Snookers lumber can convert logs into either lumber or plywood. In a given day, the mill turns out twice as many units of plywood as lumber. It makes a profit of \$30 on a unit of lumber and \$50 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of \$13390?
Snookers lumber must produce and sell ___units of lumber and ___units of plywood to make a profit of \$13390.
12.) Solve.
3y - 1 < 8y - 2
Use set builder notation to describe the complete solution.
{y|y__ __} (Type an inequality symbol, then type an integer or a fraction.)
13.) Two angles are complimentary. The sum of the measure of the first angle and one-fourth the second angle is 81 degrees. Find the measures of the angles.
What is the measure of the smaller angle? ____degrees
What is the measure of the other angle? ____degrees