Unit 5 - Objective 3 - Solving 2 Equations in 2 Unknowns Graphically

Simultaneous linear equations are equations containing the same variables.  For example:

2x - 3y = 2
3x + 2y = 3

are simultaneous equations.  We must determine all the points, or ordered pairs, that these two equations have in common.  If we graph the equations, we are looking for a common point where the two lines intersect.

Example:

1st Graph

2x - 3y = 2

 Finding the x and y intercepts:

x-intercept

2x - 3 (0) = 2
2x = 2
x = 1
So (1, 0) is the x-intercept

y-intercept

2 (0) - 3y = 2
-3y = 2
y = -2/3
So (0, -2/3) is the y-intercept

 
2nd Graph

3x + 2y = 3

 Now graph the second equation:

x-intercept

3x + 2 (0) = 3
3x = 3
x = 1
So (1, 0) is the x-intercept

y-intercept

3 (0) + 2y = 3
2y = 3
y = 3/2
So (0, 3/2) is the y-intercept

 

Find the point where these two lines intersect. It appears to be the point (1, 0).  A quick check to make sure this point satisfies these two equations.

Plug (1, 0) into the equation 2x - 3y = 2

2 (1) - 3 (0) = 2
2 = 2
This Checks

Plug (1, 0) into the equation 3x + 2y = 3

3 (1) + 2 (0) = 3
3 = 3
This Checks

So the ordered pair (1, 0) satisfies these two equations.

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