Education.com
Try
Brainzy
Try
Plus

Solving Systems of Equations and Inequalities Practice Problems

By
Updated on Oct 27, 2011

To review these concepts, go to Solving Systems of Equations and Inequalities Help.

Solving Systems of Equations and Inequalities Practice Problems

Directions: Use scratch paper and graph paper to solve the following system of equalities. You can check your answer at the end of this section.

Practice

  1. 5x + 3y = 4
    15x + dy = 21
    What value of d would give the system of equations NO solution: –9, –3, 1, or 9?
  1. y > 4
  2. y < x + 2

  3. y ≥ 5
  4. x ≤ 2

Solutions

  1. The first step in evaluating a system of equations is to write the equations so that the coefficients of one of the variables are the same. If you multiply 5x + 3y = 4 by 3, you get 15x + 9y = 12. Now you can compare the two equations because the coefficients of the x variables are the same:
        15x + 9y = 12
        15x + dy = 21
  2. The only reason there would be no solution to this system of equations is if the system sets the same expression equal to different numbers. Therefore, you must choose the value of d that would make 15x + dy identical to 15x + 9y. If d = 9, then:

        15x + 9y = 12
        15x + 9y = 21

    Thus, if d = 9, there is no solution.

  3. For y > 4, draw a dashed line at y = 4. The area of the graph above this line will satisfy the condition. For y < x + 2, graph the line. The slope is 1 and the y-intercept is 2. Start at the y-intercept (0,2) and go up 1 and over 1 (right) to plot points. This line will also be dashed because the symbol is <. The area under this line satisfies the condition. Shade the area where both conditions are satisfied:
  4. Tackling Systems Of Equations And Inequalities

  5. For y ≥ 5, draw a solid line at y = 4. The area of the graph above this line will satisfy the condition. For x ≤ 2, draw a solid line at x = 2. The area of the graph to the left of this line will satisfy the condition. Shade the area common to both conditions:
  6. Tackling Systems Of Equations And Inequalities

Add your own comment