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 Graph3x + 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.