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MFM2P1
Solving Systems – Graphically
Name_______________
Linear System: A set of two or more linear equations that are considered at the
same time.
Point of Intersection: The point where two lines cross. This point satisfies both
equations.
Ex. Solve the linear system by graphing. Than check your answer.
Equation 1: y = -2x – 5
2
Equation 2: y = x  3
3
y = -2x -5
Check: Sub the x value of the point of
intersection into both lines. Both lines
should give you the same value for y.
y
y = - 2x – 5
2
x3
3
= - 2( - 3 ) – 5
=6–5
y=1
Therefore the point of
intersection is ( -3, 1)
Graph the following linear
systems by graphing each of the
two lines. Determine the point of
intersection. Check your answer
by subbing your x value of your
point of intersection into each
equation.
1.
y = 2x + 3
y = 4x – 1
Check
y = 2x + 3
y = 4x – 1
2
x3
3
2
y = (3)  3
3
y = -2 + 3
y=1
y=
Both lines have a y value of 1 when
x = - 3 so (- 3, 1) is our solution.
2.
y = -x – 7
y = 3x + 5
Check
y = -x – 7
y = 3x + 5
Point of intersection = (
3.
,
)
y = -x +5
y=x+1
Check
y = -x + 5
y = x +1
Point of intersection = (
4.
,
)
y=x+4
y = -x – 2
Check
y=x+4
y = -x – 2
Point of intersection = (
,
)
5.
y = 2x
y = 4x + 1
Check
y = 2x
y = 4x + 1
Point of intersection = (
,
)
6. Remember lines are not always in y = mx + b form. Either rearrange the
following equations to be in y = mx +b form or solve for their x and y
intercepts to graph the following linear system and solve for the point of
intersection.
3x + y = 7
- x + 2y = 7
Point of intersection = (
,
)
7. Graph, if necessary, what is the point of intersection for the following linear
system? What special geometric property exists between these two lines?
y = 3x – 10
y = 3x – 7
Point of intersection: ___________
Geometric property: ____________
8. Fun-N-Games Video rents game machines for $10 and video games for
$3 each. Big Vid rents game machines for $7 and video games for $4
each.
Let x be the number of games rented
Let y be the total rental cost
a) Write an equation to represent the total cost for a rental from Fun-NGames Video
b) Write an equation to represent the total cost for a rental from Big Vid
c) Graph the two equations below.
Cost of Rental
Video Game Rentals
Number of Games Rented
d) What is the point of intersection? (
,
)
e) What does the point of intersection represent?