System of Equations
Systems by graphing: look at example on page 276 and summary on p.278Systems by Substitution: look at p.282, 283 y = 3x – 5OR 2x + 3y = 10 y = 2x + 2 x = 2y - 2 plug in: 3x – 5 = 2x + 2 plug in: 2(2y - 2) + 3y = 10 -2x -2x4y - 4 + 3y = 10 x – 5 = 2 7y - 4 = 10 +5 +5 +4 +4 x = 7 plug in x to find y 7y = 14 y = 2 plug in y to find x answer: (7, 16)answer: (2, 2) Systems by elimination: (look at example 1 & 5 on p.287 and 290)Use addition (or subtraction) method if both equations are in the standard form:like:2x - y = 10or3x + 2y = 12 5x + y = 11 x + 2y = 4(add these together to eliminate the y) (subtract these to eliminate the y) 2x - y = 103x + 2y = 12 + 5x + y = 11 ? ( x + 2y = 4 ) make sure you subtract all 3 terms 7x = 212x = 8 x = 3 x = 4 now plug x = 3 into either of your equationsnow plug x = 4 into either of your equations to find y to find ySometimes to use the addition or subtraction method we have to multiply 1st:Like: 2x - y = 1 we cannot eliminate x or y! x + 3y = 4if we multiply the 1st equation by 3, then we can eliminate y3(2x - y = 1) 6x - 3y = 3 + x + 3y = 4 now you can add the equations to eliminate y 7x = 7x = 1plug x = 1 into either of the equations to find yReview:31. Find the slope of the line containing: (-3, 9) and (-5, 11)32. Add: -7 + (-3) + (-12) + 1633. Use order of operations to solve: 2?- 7 + 16 ÷ (-3 + 5)34. Solve: 3(2x - 5) = 8x - 935. Solve: 6 - 2(5x - 8) = 3x - 436. Solve for y: -3x + 5y = 1537. Find the slope and y-intercept: y = 5x - 938. Find the slope and y-intercept: 2x + 4y = 839. Write the equation of the line with a y-intercept of (0, -3) and a slope of ?40. Is (-10, 0) a solution of y = -3x -30? show workSystems ReviewName:Use addition to solve for (x , y) in these system of equations: 1. 2x - y = 122. 3x + y = 113. x - y = 8 4. -5x + y = 9 3x + y = 8 7x - y = 19 x + y = 4 -2x - y = 55. 3x - 3y = 126. 4x + 5y = 167. -9x + 3y = 188. -5x - 3y = -10 5x + 3y = 4 -4x + 2y = 5 9x + 2y = -3 5x - 3y = -20Sometimes we have to multiply one of the equations 1st:Like: 2x - y = 1 we cannot eliminate x or y! x + 3y = 4if we multiply the 1st equation by 3, then we can eliminate y3(2x - y = 1) 6x - 3y = 3 + x + 3y = 4 now you can add the equations to eliminate y 7x = 7 x = 1 plug x = 1 into either of the equations to find y9. x - 2y = 410. 4x - 5y = 2211. 3x - y = 11 3x + 4y = 2 x + 2y = -1 2x + 5y = 1312. 4x + 3y = 1513. 5x - 2y = -114. 4x - 3y = 1 2x - 5y = 1 x + y = 4 8x + 5y = 13Review:15. Find the slope of the line containing: (-3, 9) and (-5, 11)16. Add: -7 + (-3) + (-12) + 1617. Use order of operations to solve: 2?- 7 + 16 ÷ (-3 + 5)18. Solve: 3(2x - 5) = 8x - 919. Solve: 6 - 2(5x - 8) = 3x - 420. Solve for y: -3x + 5y = 1521. Find the slope and y-intercept: y = 5x - 922. Find the slope and y-intercept: 2x + 4y = 823. Write the equation of the line with a y-intercept of (0, -3) and a slope of ?24. Is (-10, 0) a solution of y = -3x -30? show work ................
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