Presentation on theme: "Advanced Algebra Notes"— Presentation transcript:
1 Advanced Algebra Notes Section 3.1Solving Linear Systems by Graphing
2 Solving Linear Systems by Graphing System of two linear equationsA in two variables x and y, also called linear system, consists of two equations that can be written in the following form. When we talk about finding a we are looking for the ordered pair (x,y) that will satisfy each equation. It must work with both!Ax + By = CDx + Ey = Fsolution
3 Example 1Graph the linear system and estimate the solution. Then check the solution algebraically. 4x+y=8 2x-3y=18𝑦=−4𝑥+8−3𝑦=−2𝑥+18𝑦= −2𝑥+18 −3(3,−4)𝑦= 2 3 𝑥−6
4 Example 2 INFINITE SOLUTIONS Graph the linear system and estimate the solution. 4x-3y=8 8x-6y=16−3𝑦=−4𝑥+8𝑦= 4 3 𝑥− 8 3INFINITE SOLUTIONS−6𝑦=−8𝑥+16−3𝑦=−4𝑥+8𝑦= 4 3 𝑥− 8 3
5 Example 3 𝑦=−2𝑥+4 PARALLEL 𝑦=−2𝑥+1 NO SOLUTION Graph the linear system and estimate the solution 2x+y=4 2x+y=1𝑦=−2𝑥+4PARALLEL𝑦=−2𝑥+1NO SOLUTIONWhen lines have the same slopethey are parallel. They will not cross!They will not have a solution!
6 Example 4Graph the linear system and estimate the solution 5x-2y=-10 2x-4y=12−2𝑦=−5𝑥−10𝑦= 5 2 𝑥+ 10 2𝑦= 5 2 𝑥+5−4𝑦=−2𝑥+12𝑦= 1 2 𝑥−3(−4,−5)
7 Closing: How do you solve a system of linear equations graphically? Our solution is the point where our linesintersect. It is a coordinate point (𝑥,𝑦)If our lines do not cross, they are parallelmeaning they have no solution.If our lines are the same line, they areIntersect at every point meaning theyhave infinite solutions.Our solution has to work for both equations!!!