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Published byLouise O’Neal’ Modified over 7 years ago
Sections 3.1 & 3.2
A collection of equations in the same variables.
The solution of a system of 2 linear equations in x and y is any ordered pair, (x, y), that satisfies both equations. The solution (x, y) is also the point of intersection for the graphs of the lines in the system.
The ordered pair (2, -1) is the solution of the system below. y = x – 3 y = 5 – 3x
Exploring Graphs of Systems YOU WILL NEED: graph paper or a graphing calculator
System I.Y = 2x – 1 Y = -x + 5 II.Y = 2x – 1 Y = 2x + 1 III.Y = Y = x + 2 Graph System I at left. ◦ Are there any points of intersection? ◦ Can you find exactly one solution to the system? If so, what is it? Repeat for Systems II and III.
I. Y = 2x – 1 Y = -x + 5 Plug in your equations to Y= Press Graph
Press 2 nd, CALC Select 5: INTERSECT
FIRST CURVE? Press Enter to select the line. SECOND CURVE? Press Enter to select the 2 nd line GUESS? Move the cursor close to the point of intersection and press Enter
Intersection Point (2, 3)
Graphing a system in 2 variables will tell you whether a solution for the system exists. 3 possibilities for a system of 2 linear equations in 2 variables.
If a system of equations has at least 1 solution, it is called consistent ◦ If a system has exactly one solution, it is called independent (INTERSECTING) ◦ If a system has infinitely many solutions, it is called dependent (SAME LINE) (COINCIDING)
If a system does not have a solution, it is called inconsistent. (PARALLEL LINES) (NO SOLUTION)
Graph and Classify each system. Then find the solution from the graph. x + y = 5 x – 5y = -7 Begin by solving each equation for y.
Graph and find the intersection point like Activity 1. y = 5 – x y = Consistent & Independent
2x + y = 3 3x – 2y = 8 Solve the first equation for y.
SUBSTITUTE 3 – 2x into the second equation for y. SOLVE
Substitute 2 for x in either original equation to find y.
Solution: (2, -1) Check:
Involves multiplying and combining the equations in a system in order to eliminate a variable.
Now plug in y = 1 into either of your two original equations.
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