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# Solving Systems with Elimination

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### Solving Systems with Elimination

1. 1. Solving Systems By Elimination
2. 2. <ul><li>Both equations must be in standard form. </li></ul><ul><li>The goal is to eliminate one of the variables. </li></ul><ul><li>You can add or subtract the equations to eliminate . </li></ul>
3. 3. <ul><li>Solve the system by elimination: </li></ul><ul><li>5x – 6y = -32 </li></ul><ul><li>3x + 6y = 48 </li></ul><ul><li>8x = 16 </li></ul><ul><li>x = 2 </li></ul>Line these two equations up. Look to if any of the variables would cancel each other out if the two equations were added or subtracted.
4. 4. <ul><li>Substitute the x back into one of the equations to find the other variable. </li></ul><ul><li>5(2) – 6y = -32 </li></ul><ul><li>y = 7 </li></ul><ul><li>The point of intersection is (2, 7) </li></ul>
5. 5. <ul><li>Check your work. </li></ul><ul><li>Does the point work in both equations? </li></ul>
6. 6. <ul><li>How do we solve? </li></ul><ul><li>x + y = 6 </li></ul><ul><li>x + 3y = 10 </li></ul><ul><li>Subtract (or multiply 2 nd equation by -1) </li></ul><ul><li>And the solution is . . . </li></ul><ul><li>(4, 2) </li></ul>
7. 7. <ul><li>How do we solve? </li></ul><ul><li>5x + 6y = 54 </li></ul><ul><li>3x - 3y = 17 </li></ul><ul><li>Multiply the 2 nd equation by 2 </li></ul><ul><li>And the solution is . . . </li></ul><ul><li>(8, 7/3) </li></ul>
8. 8. <ul><li>How do we solve? </li></ul><ul><li>-a + 2b = -1 </li></ul><ul><li>a = 3b - 1 </li></ul><ul><li>1 st , get that 2 nd equation in standard form. a – 3b = -1 </li></ul><ul><li>And the solution is . . . </li></ul><ul><li>(5, 2) </li></ul>
9. 9. <ul><li>How do we solve? </li></ul><ul><li>2k – 3c = 6 </li></ul><ul><li>6k – 9c = 9 </li></ul><ul><li>Multiply 1 st row by -3. </li></ul><ul><li>And the solution is . . . </li></ul><ul><li>No solution </li></ul><ul><li>What do you notice that helps you understand this is no solution? </li></ul>
10. 10. <ul><li>How do we solve? </li></ul><ul><li>x + 4y = 1 </li></ul><ul><li>3x + 12y = 3 </li></ul><ul><li>Multiply the 1 st one by -3 </li></ul><ul><li>And the solution is . . . </li></ul><ul><li>Infinite number of solutions </li></ul><ul><li>What do you notice that helps you understand this is infinite number of solutions? </li></ul>