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