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Math project

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Math project

1. 1. 3.2 Solving Systems Algebraically By: Jonathan O. Awoloi
2. 2. Substitution method <ul><ul><li>Step 1-Solve one of the equations for a variable </li></ul></ul><ul><ul><li>Step 2-Substitute the answer to the variable from step 1 into the other equation and solve for the other variable </li></ul></ul><ul><ul><li>Step 3-Substitute the answer from step 2 into the equation for step 1( the original, not the solved one) </li></ul></ul>
3. 3. Example of Substitution method <ul><ul><li>Solve the system using substitution </li></ul></ul><ul><li>3x-y=-2 -y=-2-3x or y=2+3x 3(1)-y=-2 </li></ul><ul><li>-y=-5 </li></ul><ul><li>y=5 </li></ul><ul><li>5x+2y=15 5x+2(2+3x)=15 5(1)+2y=15 </li></ul><ul><li>5x+4+6x=15 5+2y=15 </li></ul><ul><li>11x+4=15 2y=10 </li></ul><ul><li>11x=11 so x=1 y=5 </li></ul><ul><li>Answer: (1,5) is the same as x=1 and y=5 </li></ul>
4. 4. Elimination method <ul><ul><li>Step 1- Multiply one or both of the equations by a number that can give the same numbers as coefficients for one of the variables, but one of the coefficients must be positive and one negative </li></ul></ul><ul><ul><li>Step 2- Add the results of step 1, so the two opposite numbers will cancel out leaving one variable. Solve for this variable. </li></ul></ul><ul><ul><li>Step 3- substitute the result of step 2 into one of the original equations and solve for the other variable </li></ul></ul>
5. 5. Example of elimination method <ul><ul><li>Solve the system using the elimination method </li></ul></ul><ul><li>4x-2y=16 2(4x-2y=16) 8x-4y= -32 8(-4)-4y=32 </li></ul><ul><li>-32-4y=32 </li></ul><ul><li>+ -4y=0 y=0 </li></ul><ul><li>-3x+4y=12 -3x+4y= 12 -3(-4)+4y=12 </li></ul><ul><li>5x= -20 12+4y=12 </li></ul><ul><li>x= -4 4y=0 y=0 </li></ul><ul><li>Answer:(-4,0) is the same as X=-4 and y=0 </li></ul>
6. 6. source <ul><ul><li>Mcdougell Littell Algebra 2 Mathbook </li></ul></ul><ul><ul><ul><li>Pages 160, 161, and practice on page 164 </li></ul></ul></ul>
7. 7. Comments <ul><li>Feel free to comment and add to the information if you feel so </li></ul>
8. 8.   <ul><li>  </li></ul>