Download Solving Equations, Part II (Systems and Inequalities)

Project 7: Solving Equations, Part II (Systems and Inequalities) Solving Systems of Linear Equations: For each of the pairs of equations, first choose which approach is likely easier to solve the system of equations (substitution or addition). Then use that approach to solve the system of equations for both x and y. And finally check your work by substituting your solution into both equations. Equations of the Which lines: approach is likely best? (substitution or addition) 1
5
Which variable is best Solve to get a number value for to solve for first? the first variable: For substitution: Using which equation? Now solve for that variable in terms of the other! 3 1
6
4
2
3
2
3
3
2
4
2
4
2
3
2
3
9 3
2
3
3
4
6 8
3
Rewrite final solution here: Check that solution by substituting both the x and y values into both equations, and making sure that this makes both equations true: For addition: What numbers would you have to multiply each equation by to solve for that variable? 3
Solve to get a number value for the second variable: 2
Solving Inequalities: Complete the chart, using the example in the first row as a guide: Original inequality and graph 5
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6
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5
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5
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Operation 6 5 6 Add 2 to each side
Add 2 to each side
Add 2 to each side
Left: 53; Right: 64 Add 2 to each side
Add 2 to each side
Multiply each side by 2
Left: 510; Right: 612
Multiply each side by 2
Multiply each side by 2
Multiply each side by 2
6 5 6 6 5 6 6 5 6 Left: 5-10; Right: 6-12
5 3<4
No
10<12
Yes
-10>-12
Divide each side by 2
Divide each side by 2
5 No
6 6<8
6 No
Multiply each side by 2
Multiply each side by 2
Divide each side by 2
Left: 52.5; Right: 63
6 New
inequality resulting from operation Add 2 to each side
Left: 57; Right: 68
6 Graph what happens to each, before and Did this after the operation, on the number line operation flip the number line? Divide each side by 2
Left: 5-2.5; Right: 6-3 No
2.5<3
Yes
-2.5>3
Divide each side by 2
Divide each side by 2
Based on the patterns observed in the above chart, circle the operations below that flip the number line (and the inequality sign): 





Adding a positive number Adding a negative number, or subtracting a positive number Multiplying by a positive number Multiplying by a negative number Dividing by a positive number Dividing by a negative number Solving specific inequalities: For each of the following inequalities, solve the inequality. Then graph the solution set. Solve for : 10
2
5 10
10 2
5
10 10
10 2
10
10 10
10 2
10
10 10
10
2
0 0 2 2 2
2
2 3
0 0
3
3
3
1
0 0 3 2
9 5 Check answer by testing two values: Testing 1, which should be false, because 1 0: 10
1
2
1
5 10 1 2 4 11 8  FALSE! Testing 1, which should be true, because 1 0: 10
1
2 1
5 9 2 6 9 12  TRUE! 5
3
3 2
4
3
4
2 12
2 3
1
8
1
5 2
4
2 3
5
2
10 Graph the solution set