Solving systems by graphing8/27/2023 ![]() It looks as if the lines intersect at (32,20). Let y be the price (in dollars) per roll. Find the price per bundle of shingles and the price per roll of roofing paper. In a second purchase (at the same prices), the contractor buys 8 bundles of shingles for $256. Did they work? (3,1) is the solution.Ī roofing contractor buys 30 bundles of shingles and 4 rolls of roofing paper for $1040. Remember to substitute those values back into your original equations. y = x – 2 Equation 1 y = -x + 4 Equation 2 The lines intersect at (3,1). Solve the system of linear equations by graphing. 1)ģ) Check your work: y = -2x Equation y = 4x – Equation 2 3 = -2(1) + 5 3 = 3 3 = 4(1) – 1 3 = 3 (1,3) is the solution to the system.ĩ Example 2: Solving a System of Linear Equations by Graphingī) Solve the system of Linear equations by graphing: 2x + y = 5 Equation 1 3x – 2y = 4 Equation 2 1) 2x + 0 = 5 2x = 5 x = 5/2 = 2 ½ 2(0) + y = 5 y = 5 3x – 2(0) = 4 3x = 4 x = 4/3 = 1 1/3 3(0) – 2y = 4 -2y = 4 y = -2 2) The two lines intersect at point (2, 1).ģ) Check your work: 2x + y = Equation x – 2y = Equation 2 2(2) + 1 = 5 5 = 5 3(2) – 2(1) = 4 6 – 2 = 4 4 = 4 (2,1) is the solution to the system. Step 3: Check the point from step 2 by substituting for x and y in each equation of the original system.ħ Example 2: Solving a System of Linear Equations by GraphingĪ) Solve the system of Linear equations by graphing: y = -2x + 5 Equation 1 y = 4x – 1 Equation 2 2) The two lines intersect at point (1, 3). Step 2: Estimate the point of intersection. Step 1: Graph each equation in the same coordinate plane. (1,4) is a solution to the system of linear equations.Ħ Solving Systems of Linear Equations by Graphing Equation 1 y = -2x - 4 0 = -2(-2) - 4 0 = 4 - 4 0 = 0 Equation 2 y = x + 4 0 = 0 = 2 Since the ordered pair (-2,0) is not a solution of each of the equations, it is NOT a solution to the linear system.ĥ You try! Tell whether the ordered pair is a solution to the system of linear equations. ![]() b) (-2,0) y = -2x – 4 Equation 1 y = x + 4 Equation 2 Substitute -2 in for x and 0 in for y in each equation. Tell whether the ordered pair is a solution of the system of linear equations. ![]() Equation 1 x + y = 7 2 + 5 = 7 7 = 7 Equation 2 2x – 3y = -11 2(2) – 3(5) = -11 4 – 15 = -11 -11 = -11 Since the ordered pair (2,5) is a solution of each of the equations, it is a solution to the linear system. ![]() ![]() (2,5) x + y = Equation 1 2x – 3y = Equation 2 Substitute 2 in for x and 5 in for y in each equation. \nonumber \]Ĭomparing \(y =(−2/3)x+2\) with the slope-intercept form \(y = mx+b\) tells us that the slope is \(m = −2/3\) and they-intercept is \((0,2)\).1 5.1 Solving Systems of Linear Equations by GraphingĪ set of two or more linear equations in the same variables Example: x + y = 7 Equation 1 2x – 3y = Equation 2 Solution of a system of Linear Equations In two variables, is an ordered pair that is the solution to each equation in the system ![]()
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