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Name: Date: Systems of Equations: Substitution Method Solve each system of equations using the Substitution Method. a) b) 𝑦 = 5𝑥 − 7 −3𝑥 − 2𝑦 = −12 2𝑦 = 𝑥 + 3 𝑥=𝑦 Solution: ____________ Solution: ____________ Check first equation: Check first equation: Check second equation: Check second equation: c) d) 𝑦 =𝑥−2 2𝑥 + 2𝑦 = 4 𝑦 = 3𝑥 + 6 𝑥 = 3𝑦 + 6 Solution: ____________ Solution: ____________ Check first equation: Check first equation: Check second equation: Check second equation: Name: Date: Review – Rock these. a) Create a system of equations that contains parallel lines. b) Is the line x = 4 a function? Explain why or why not. c) Find the equation of the line between the points (2, 7) and (-3, -8). d) Find the equation of the line perpendicular 3 to 𝑦 = 4 𝑥 + 7 which passes through the point (3, 5). Equation of the line: _______________ e) Solve for x. f) How many solutions does this system of equations have? -3(7 + x) = -2(x – 5) 𝑦 = −3𝑥 + 4 𝑦 = 3𝑥 − 5 No. of solutions: ________ How can you tell? x = __________ g) Put this equation in slope-intercept form. h) Does this system of equations contain parallel lines, perpendicular lines, or neither? 6x – 4y – 9 = 0 2 𝑦 = 3𝑥 + 8 6 = 3𝑦 − 2𝑥 Parallel Perpendicular Neither Name: Date: Answer Key a) b) c) d) x = 2, y = 3 x = 3, y = 3 x = 2, y = 0 x = - 3, y = - 3 a) check your answer on Desmos! b) No, because the same input (x) generates more than 1 output (y) c) y = 3x + 1 −4 d) 𝑦 = 3 𝑥 + 9 e) x = – 31 f) The system has 1 solution. I can tell this because the slopes of the 2 lines are different, therefore the lines intersect at exactly 1 point. 3 9 g) 𝑦 = 2 𝑥 + 4 h) The lines are parallel.