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Solving Systems of Equations by Graphing
Practice test 1 – Sept 8 LT # 1 – Sept 10
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Recall: SLOPE-INTERCEPT FORM y = mx + b slope y-intercept x + 2y = 6
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Convert to slope-intercept form.
x + 2y = 6 2y = -x + 6 y = -1/2 x + 3
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Y = -1/2 x + 3
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. (1,5) y = 2x + 3 2) Obtain a second point using the slope, m.
1) Plot the point (0,3). 2) Obtain a second point using the slope, m. (for every 2 rise, 1 run) 3) Draw a line through the two points. y-intercept slope . (1,5) (0,3) Write m as a fraction, and use rise over run, starting at the point containing the y-intercept, to plot this point. We express the slope, 2, as a fraction.
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is a System of Linear Equations in two variables (x and y)
The solution to the system is the ordered pair (1, 2) because it satisfies both equations.
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Simultaneous Linear Equations or System of Linear Equations
is a collection of linear equations with the same set of unknowns They are solved by finding values that work for both variables (x and y) at the same time (simultaneously).
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Solution of a System of Equations
A solution of a system of linear equations in two variables is an ordered pair (x, y) that makes BOTH equations true. A system of equations can have 0, 1, or an infinite number of solutions.
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x + y = 3 y = 3x + 3 (0, 3) x + y = 1 2y = -2x + 2 (2, -1) x + y = 8
Tell whether the ordered pair is a solution of the system of equations. Justify your answer. x + y = 3 y = 3x + 3 (0, 3) x + y = 1 2y = -2x + 2 (2, -1) x + y = 8 x – 7 + y = 0 (4, 4)
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Intersecting Lines 1 Solution: (3, -1)
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Parallel Lines No solution: { } or Ø
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Infinitely many solutions:
Conciding Lines Infinitely many solutions: {(x, y)| x + y = 2} READ AS: The set of all ordered pairs (x, y) such that “x + y = 2”.
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GRAPH SLOPE Y-INTERCEPT Intersecting Different Same or Different Coinciding Same Parallel
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Solutions of a System of
Linear Equations Consistent At least 1 solution Inconsistent No solution Dependent Infinite solutions Independent Unique/1 solution
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EXISTENCE OF SOLUTION Number OF SOLUTIONS SLOPE Y-INTERCEPT
Consistent Independent (One - Point of Intersection) Different Same or Different Dependent (Infinite - All points that lie on the line) Same Inconsistent No solution
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Solving Systems of Linear Equations Using Graphical Method
To find the solution of a system of linear equations graphically, determine the coordinates of the point of intersection of both graphs.
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The Number of Solutions to a System of Two Linear Equations
Existence of Solution Number of Solutions Graph Consistent and independent Exactly one ordered-pair solution Inconsistent No solution Consistent and dependent Infinitely Many Solutions
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Work in Pairs Without graphing, determine the ff:
a) existence of solution (consistent/inconsistent) b) number of solutions (dependent/independent) c) graph of the system (intersecting, parallel, coinciding)
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2) 3x + y = x – y = 3
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4) 4x + y = 2 4x + y = -3
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6) 3x – 2y = x + 3y = 9
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8) 3x + 2y = x + y = 2
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10) 2x + 5y = x – 2y = 9
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12) 3x – 4y = x – y = 16
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- Review all files uploaded in Edmodo - Study Examples 1 & 2 NSM Bk2 p
- Review all files uploaded in Edmodo - Study Examples 1 & 2 NSM Bk2 p Review Questions # 5, 6, and 7 page 258
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Online Self-Assessment
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