By LearningExpress Editors

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 **

- 5
*x*+ 3*y*= 4

- 15

*x*+

*dy*= 21

- What value of

*d*would give the system of equations NO solution: –9, –3, 1, or 9?

*y*> 4*y*≥ 5

*y* < *x* + 2

*x* ≤ 2

**Solutions**

- 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 5
*x*+ 3*y*= 4 by 3, you get 15*x*+ 9*y*= 12. Now you can compare the two equations because the coefficients of the*x*variables are the same:- 15

*x*+ 9*y*= 12- 15

*x*+ d*y*= 21 - 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: - 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:

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 15*x* + d*y* identical to 15*x* + 9*y*. If *d* = 9, then:

- 15

*x*+ 9

*y*= 12

- 15

*x*+ 9

*y*= 21

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

From Express Review Guides: Algebra II. Copyright © 2007 by LearningExpress, LLC. All Rights Reserved

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