6-1 So l vi n g Sy st em s b y Gr ap h i n g
T
Quick Review
One way to solve a system of linear equations is by graphing
each equation and finding the intersection point of the
graph, if one exists.Ex a m p l e
What is the solution of the system? y = - 2x + 2
y = 0.5x — 3
y = -2 x + 2 Sl o p e i s - 2 ; y - i n t e r c e p t i s 2.
y = 0.5x - 3 Sl o p e i s 0. 5 ; y - i n t e r c e p t i s - 3.The lines appear to intersect at
(2, —2). Check if (2, —2) makes
both equations true.
-2 = - 2 ( 2 ) + 2
-2 = 0.5(2) - 3
So, the solution is ( 2 , - 2 ).Ex e r c i se s
Solve each system by graphing. Check your answer.- y = 3x+13 5. y = - x + 4
6. y = 2x + 3
1
3J
8. y=-2x - 21
y = x - 7y = 3x + 12- y — 1.5x + 2
4.5x — 3y = —9 - y = x + 1
2x — 2 y = —2 - Songwrit ing Jay has written 24 songs to date. He
writes an average of 6 songs per year. Jenna started
writing songs this year and expects to write about
12 songs per year. How many years from now will
Jenna have written as many songs as Jay? Write and
graph a system of equations to find your answer. - Reasoning Describe the graph of a system of
equations that has no solution.
6-2 Solving System s Using Substitution
Quick Review
You can solve a system of equations by solving one
equation for one variable and then substituting the
expression for that variable into the other equation.
Ex a m p l e
What is the solution of the system?
3x + 3y = - 18
3x + 3y = -1 8 Write the second equation.
3x+3(-|x) = -18
2 x= -18
x= —9y = 3The solution is (-9, 3).
Su b st i t u t e - | x f o r y.
Si m p l i f y.
So l v e f o r x.
Su b st i t u t e - 9 f o r x i n t h e
first equation.Ex e r c i s e s
Solve each system using substitution. Tell whether the
system has on e solution, infinitely m any solutions, or
no solution.12. y = 2 x — 1
2 x + 2 y = 22- 2 x + y = -12
—4x — 2y = 30 - y = x — 7
3x — 3y = 21
13. -x + y = -13
3x-y = 19
-ic 1 7 ,515. g y = o * + o
17.3
x - 3y = 5
3x + y = —13
—2x + 5y = -5 4- Business The owner of a hair salon charges $20
more per haircut than the assistant. Yesterday the
assistant gave 12 haircuts. The owner gave 6 haircuts.
The total earnings from haircuts were $750. How
much does the owner charge for a haircut? Solve by
writing and solving a system of equations.
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