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# Alg2 lesson 3-1

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### Alg2 lesson 3-1

1. 1. A system of linear equations is a group of equations that are considered at the same time.<br />The solution of a system of linear equations is the set of ordered pairs that make all equations in the system true.<br />
2. 2. Solve the system of equations by graphing.<br />x – y = 5<br />x + 2y = -4<br />x – y = 5<br />5 – 0 =5<br /> (5, 0)<br />0 –(-5) = 5<br /> (0, -5)<br />x + 2y = -4<br />0 + 2(-2) = -4<br /> (0, -2)<br />-4 + 2(0) = -4<br /> (-4, 0)<br />The solution is consistent and independent<br />The solution appears to be (2, -3)<br />Example 1-1a<br />
3. 3. Check the solution<br />x – y = 5<br />x + 2y = -4<br />x – y = 5<br />2 – -3 =5<br />2 + 3 = 5<br />5 = 5<br />x + 2y = -4<br />2 + 2(-3) = -4<br />2 – 6 = -4<br />-4 = -4<br />Example 1-1a<br />
4. 4. Solve the system of equations by graphing.<br />y = 2x – 3<br />y = -2x + 5<br />The solution appears to be (2, 1)<br />y = 2x – 3<br />1 = 2(2) – 3<br />1 = 4 – 3<br />1 = 1<br />y = -2x + 5<br />1 = -2(2) + 5<br />1 = -4 + 5<br />1 = 1<br />The solution is consistent and independent<br />Example 1-1a<br />
5. 5. Solve the system of equations by graphing.<br />0 – 2(0) = 0<br /> (0, 0)<br />2 – 2(1) = 0<br /> (2, 1) <br />3 + 3 = 6<br /> (3, 3)<br />1 + 5 = 6<br /> (1, 5)<br />The solution is consistent and independent<br />The solution appears to be (4, 2)<br />Example 1-1a<br />
6. 6. Original equations<br />Replace x with 4and y with 2.<br />Simplify.<br />Check Substitute the coordinates into each equation.<br />Answer: The solution of the system is (4, 2).<br />Example 1-1a<br />
7. 7. Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.<br />Write the equations in slope-intercept form.<br />Parallel lines<br /> No solution<br />The system is inconsistent.<br />Example 1-5a<br />
8. 8. Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.<br />Write the equations in slope-intercept form.<br />Since the equations are equivalent, their graphs are the same line. The solution is consistent and dependent.<br />Example 1-4a<br />
9. 9. Describe the solution to the system.<br />{(x, y) |<br />}<br />Example 1-4a<br />
10. 10. Let<br />Fund-raisingA service club is selling copies of their holiday cookbook to raise funds for a project. The printer’s set-up charge is \$200, and each book costs \$2 to print. The cookbooks will sell for \$6 each. How many cookbooks must the members sell before they make a profit?<br />What is the independent variable? Cookbooks<br />What is the dependent variable? Dollars<br />Example 1-2a<br />
11. 11. price per book<br />number of books.<br /> is<br />times<br />\$ of income<br />Let<br />\$ to produce<br /> is<br />cost per book<br />plus<br />set-up charge.<br />Fund-raisingA service club is selling copies of their holiday cookbook to raise funds for a project. The printer’s set-up charge is \$200, and each book costs \$2 to print. The cookbooks will sell for \$6 each. How many cookbooks must the members sell before they make a profit?<br />y<br />=<br />2x<br />+<br />200<br />y<br />=<br />6<br />x<br />Example 1-2a<br />
12. 12. Solve the system:<br />y = 2x + 200<br />y = 6x<br />The graphsintersect at (50, 300). This is the break-evenpoint. If the groupsells less than 50 books, they will lose money.If the groupsellsmore than 50 books, they will make aprofit.<br />Example 1-2a<br />