Download Aim #53: How do we solve a system of linear equations graphically

Aim #53: How do we solve asystem of linear equations
graphically?
(Unit 6 - Systems of Equations/Inequalities)
Do Now: List 3 ordered pairs that lie on the line of each
equation.
a) x + y = 6
b)
x-y=6
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Solving Systems of Linear Equations Graphically
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What values for x and y would work in both linear equations ?
x+y=6
SOLUTION:
x-y=6
(6, 0)
System of Linear Equations: 2 linear equations
with the same variables
Solution of a System
of Linear Equations: ordered pair (x, y) that makes both linear
equations true (where the lines intersect)
Lets solve the following system graphically!
x + y = 6
x - y = 6
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1. y + 8 = x
2x - 3y = 15
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2. x + 2y = 16
-2y = x - 10
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3. y = -4x - 1
3y + 3 = -12x
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4. Without solving, state the number of solutions for each system of equations.
a) x + y = 6
b) 2y = 4x + 12
c) y = -3x + 1
2x + 2y = 12
y = 2x + 5
y = 3x + 1
Number of
Solutions
One Solution
No Solution
Infinitely
Many Solutions
Graph
Equation
the lines
intersect
different slopes
the lines are
same slope
different y-intercepts
parallel
the lines are
the same
same slope
same y-intercept
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Sum it up, Ms. C!:
A system of equations can have ____ solution, ____
solution, or ______________ solutions.
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