Download presentation
Presentation is loading. Please wait.
Published byMaximilian Hancock Modified over 9 years ago
2
System of Equations 2 (or more) equations, each of which has 2 (or more) variables
4
Our goal is normally to find a the values of the variables that work in both equations.
5
In most cases you can think of this as the point where two lines cross. (x,y) is the solution to the system of equations.
6
There are lots of ways to solve systems of equations. One way is by graphing. Carefully graph both lines on the same axes. Find the point where they cross.
7
Solve y = 2x + 2 y = x – 1
8
Solve y = 2x + 2 y = x – 1 y = 2x + 2 y-intercept = 2 slope = 2 / 1 y = x – 1 y-intercept = -1 slope = 1 / 1
9
The solution is (3, -4)
10
Solve y = x + 2 y = -x + 4 y = x + 2 y-intercept = 2 slope = 1 / 1 y = -x + 4 y-intercept = 4 slope = -1 / 1
11
The solution is (1,3)
12
Solve x + 2y = 5 2x + y = 4
13
Solve x + 2y = 5 2x + y = 4 Find the intercepts.
14
Solve x + 2y = 5 2x + y = 4 Find the intercepts. x + 2y = 5 (0,2.5)and (5,0) 2x + y = 4 (0,4) and (2,0)
15
The solution is (1,2)
16
Solve 2x + 2y = 6 4x – 6y = 12
17
Solve 2x + 2y = 6 4x – 6y = 12 Intercepts 2x + 2y = 6 (0,3) and (3,0) 4x – 6y = 12 (0,-2) and (3,0)
18
We can tell without even finishing the graph that (3,0) is the solution.
19
Solve 3x + 2y = 12 3x + 2y = 6
20
Solve 3x + 2y = 12 3x + 2y = 6 Intercepts 3x + 2y = 12 (0,6) and (4,0) 3x + 2y = 6 (0,3) and (2,0)
21
These are parallel lines. They both have a slope or -3 / 2. They never intersect, so there is no solution.
22
It’s also possible to have infinitely many solutions, which would mean you have different expressions for the same line. For example:5x + 2y = 10 y = -5 / 2 x + 5
23
There are lots of word problems that involve systems of equations. For instance … Two tacos and a burrito cost $8. One taco and two burritos cost $10. How much is a taco, and how much is a burrito?
24
Two tacos and a burrito cost $8. One taco and two burritos cost $10. How much is a taco, and how much is a burrito? 2t + 1b = 82x + 1y = 8 1t + 2b = 101x + 2y = 10
25
2x + 1y = 8 1x + 2y = 10 The solution is (2,4)
26
Two tacos and a burrito cost $8. One taco and two burritos cost $10. How much is a taco, and how much is a burrito? (2,4) means a taco costs $2 and a burrito costs $4.
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.