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Published byAudrey Longsworth Modified over 2 years ago

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Graph Linear Systems Written in Standard Form

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Types of Linear Equations O Slope Intercept Form: y = mx + b O You have used this one the most. O If you have your slope and y-intercept, you can graph a line or even a system of equations (two lines). O Standard Form: Ax + By = C O “A” is the coefficient of “x.” O “B” is the coefficient of “y.” O “C” is a number (a constant)

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What type of Equation is this? 1. y = 2x x – 4y = x + 19y = 5 4. y = ½ x x + y = 3 6. y = - 2 / 3 x – 9 / 2 1. Slope-Intercept Form 2. Standard Form 3. Standard Form 4. Slope-Intercept Form 5. Standard Form 6. Slope-Intercept Form

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Standard Form: Ax + By = C O To graph an equation in standard form, you use the x- and y-intercepts. O The x-intercept is: “What is x if y is zero?” (#, 0) O The y-intercept is: “What is y if x is zero?” (0, #)

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Find the x- and y- intercepts of the following equations: 1. 4x + 2y = x – y = x + 4y = x – 12y = (3, 0) & (0, 6) 2. (2, 0) & (0, -6) 3. (-4, 0) & (0, 5) 4. (-4, 0) & (0, 3)

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It is where the two lines intersect. What does “Solving a Linear System” mean?

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Graph to solve the linear system. 2x – y = 2 4x + 3y = 24 O Since the equations are in standard form, find the x- and y- intercepts to graph. 2x – y = 2 2x – 0 = 2 2x = 2 x = 1 (1, 0) 2x – y = 2 2(0) – y = 2 -y = 2 y = -2 (0, -2) 4x + 3y = 24 4x + 3(0) = 24 4x = 24 x = 6 (6, 0) 4x + 3y = 24 4(0) + 3y = 24 3y = 24 y = 8 (0, 8)

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2x – y = 2 Intercepts are (1, 0) & (0, -2) 4x + 3y = 24 Intercepts are (6, 0) & (0, 8) Graph to solve the linear system. Where do the lines intersect? (3, 4) is the solution to this system of linear equations.

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Graph to solve the linear system. -4x – 2y = -12 4x + 8y = -24 O Since the equations are in standard form, find the x- and y- intercepts to graph. -4x – 2y = x – 2(0) = x = -12 x = 3 (3, 0) -4x – 2y = (0) – 2y = y = -12 y = 6 (0, 6) 4x + 8y = -24 4x + 8(0) = -24 4x = -24 x = -6 (-6, 0) 4x + 8y = -24 4(0) + 8y = -24 8y = -24 y = -3 (0, -3)

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-4x – 2y = -12 Intercepts are (3, 0) & (0, 6) 4x + 8y = -24 Intercepts are (-6, 0) & (0, -3) Graph to solve the linear system. Where do the lines intersect? (6, -6) is the solution to this system of linear equations.

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