Lesson 2.1
different slope
same slope,
same intercept
same slope,
different intercept
Classify Systems
A. Graph the system of equations and describe it as
consistent and independent, consistent and dependent, or
inconsistent.
x–y=5
x + 2y = –4
Write each equation in slope-intercept form.
Since the two lines have different slopes, the system is
consistent and independent.
Classify Systems
B. Graph the system of equations and describe it as
consistent and independent, consistent and dependent, or
inconsistent.
9x – 6y = –6
6x – 4y = –4
Write each equation in slope-intercept form.
Since the equations have the same slopes and same
intercepts the system is consistent and dependent.
Solve the system of equations by graphing.
x – 2y = 0
x+y=6
Write each equation in slope-intercept form.
The graphs appear to
intersect at (4, 2).
Use the substitution method to solve the system of equations.
4x - 3y = 11
x+y=8
You can solve the second equation
for either y or x. If you solve for x,
the result is x = 8 - y. Then substitute
8 - y for x in the first equation.
4x - 3y = 11
4(8 - y) - 3y = 11 x = 8 - y
-7y = -21
y=3
The solution is (5, 3).
Now substitute 3 for y in
either of the original
equations, and solve for x.
x+y=8
x+3=8
x=5
y=3
Use the elimination method to solve the system of equations.
3x - 2y = 18
4x + 3y = -10
One way to solve this system is to multiply both
sides of the first equation by 3, multiply both
sides of the second equation by 2, and add the
two equations to eliminate y. Then solve the
resulting equation.
Now substitute 2 for x in either of
the original equations.
3(3x - 2y)= 3(18)  9x - 6y = 54
2(4x + 3y)= 2(-10)  8x + 6y = -20
17x =34
x= 2
3x - 2y = 18
3(2) - 2y = 18
-2y = 12
y = -6
The solution is (2, -6).
x=2
Example 5.
AMC Homes, Inc. is planning to build three- and four-bedroom
homes in a housing development called Chestnut Hills. Consumer
demand indicates a need for four times as many four-bedroom homes
as for three-bedroom homes. The net profit from each three-bedroom home
is $15, 000 and from each four-bedroom home is $18,000. If AMC Homes
must net a total profit of $17.4 million from this development, how many homes
of each type should they build?
Solution.
x = three bedroom homes
y = four bedroom homes
15,000x + 18,000y =17,400,000 Reduce by 1,000
4x = y
15x + 18y = 17,400
4x = y
15x + 18(4x) = 17,400
15x + 72x = 17,400
87x = 17,400
x = 200
y = 4(200)=800
They should build 200 three-bedroom homes and 800 fourbedroom homes.