Systems of Linear Equations An intersection of lines

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Systems of Linear EquationsAn intersection of
lines

• Mr. Bitter

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Graphing Systems of Linear Equation
system of linear equation

• Two or more linear equations form a system of
  linear equation
• A solution of the system is any ordered pair that
  is a solution of each equation in the in in the
  system.
• You can solve some systems of equations by
  graphing the equations on a coordinate plane and
  identifying the points of intersection.

(1,0)
y
Solution

• Solve some systems of equations by graphing
  (identify the point(s) of intersection.)

x
3
? Example 1

• Solve the system yx1 and y2x 4 by graphing.
• Step 1 Find the x and y-intercepts for the first
  line (y-intercept first.)

Let x 0 To solve for the y-intercept
When x is 0, the y-intercept is 1
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? Example 1

• Solve the system yx1 and y2x 4 by graphing.
• Step 1 Next, find the x-intercept for the first
  line.

Now, let y 0 to find the x-intercept
When y is 0, the x-intercept is 1
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? Example 1

• Solve the system y x 1 and y2x 4 by
  graphing.
• Step 2 Find the x and y-intercepts for the
  second line (y-intercept first.)

y
Let x 0 To solve for the y-intercept
x
When x is 0, the y-intercept is 4
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? Example 1

• Solve the system y x 1 and y2x 4 by
  graphing.
• Step 2 Next, find the x-intercept for the 2nd
  line.

y
Let y 0 To solve for the x-intercept
x
When y is 0, the x-intercept is -2
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? Example 1

• Solve the system y x 1 and y2x 4 by
  graphing.
• Step 3 Find the point of intersection.

The lines intersect at one point, (-1,2). The
solution is (-1,2).
y
(-1,2)
x
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? Example 1

• Solve the system y x 1 and y2x 4 by
  graphing.
• Step 4 Check to see whether (-1,2) is true for
  both equations.

Replace x with -1 and y with 2
The Solution checks