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Unit 1. Solving system of equations. System of equations. Define : system of equations - a set of two or more equations Define : solution of a system - ordered pair(s) that make all the equations true. Key concept : the solution to a system is where the graphs intersect. Lines are Parallel - PowerPoint PPT Presentation
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SOLVING SYSTEM OF EQUATIONS
Unit 1
System of equations
Define: system of equations- a set of two or more equations
Define: solution of a system- ordered pair(s) that make all the equations true.
Key concept: the solution to a system is where the graphs intersect.
Lines intersect1 solution
Lines are ParallelNo solution
Lines coincideInfinitely many solutions
Solve by Substitution
42
1353
yx
yx
42
1353
xy
yx
13)42(53 xx
1320103 xx
77 x
20 20
1x
4)1(2 y 2y
135)1(3 y 2y
)2,1(
Solve by Elimination
42
1353
yx
yx
)4(5)2(5
1353
yx
yx
20510
1353
yx
yx
x7
1x
4)1(2 y 2y
135)1(3 y 2y
)2,1(
1353 yx20510 yx
7
Would it change the solution if we solved by eliminating the x instead of the y?
System word problem
Mr. Smith bought 2 lbs of jelly and 3 lbs of peanut butter. He paid $26.35. Mrs. Sing paid $18.35 for 1.5 lbs of jelly and 2 lbs of peanut butter. What was the price per pound of each item?
1st write two equations that model the above situation.
~Mr. Smith’s shopping trip~Mrs. Sing’s shopping trip
35.1825.1
35.2632
pj
pj
Then solve the system by using any method. $4.70/lb for Jelly$5.65/lb for Peanut Butter