7.1  Solving Linear Systems by Graphing

Mrs. Agriesti's Algebra

Goal: To solve systems of linear equations by graphing.

System of equations -   two equations with the same variables that are solved simultaneously.

Example 1:       4x  - 7y = 21
                       11x + 3y =  -9

Since these equations are written in standard form I will graph by finding the intercepts.  (See section 4.3 for help.)

1st equation:   
    When x is 0, y must be -3.  This gives me the point (0, -3). 
    When y is 0, x must be 21/4 or 5 1/4.  This is the point (5 1/4, 0).
    Plot the points and draw the line.

2nd equation:
    When x is 0, y must be -3.  This gives me the point (0, -3).
    When y is 0, x must be -9/11.  This gives the point (-9/11, 0).
    Plot the points and draw the line.

The point of intersection of the two lines is the solution.  The solution of this system is (0, -3).

Check:   4(0) - 7(-3) = 21?           11(0) + 3(-3) = -9?
                 0   +  21 = 21?                   0  - 9  =  -9?
                       21 = 21ü                     -9 = -9ü

Example 2:     y = 2x - 4
                       y = (-1/2)x + 1

Since these equations are written in slope-intercept form I will graph by plotting the y-intercept and using the slope.  (See section 4.5 for help.)

1st equation:   
    The y-intercept is -4.  Plot it.
    The slope is 2, rise 2 and go right 1 to find another point.
    Draw the line.

2nd equation:
    The y-intercept is 1.  Plot it.
    The slope is -1/2; go down 1 and go right 2 to find another point.
    Draw the line.

The point of intersection of the two lines is the solution.  The solution of this system is (2, 0).

Check:   0 = 2(2) - 4?           0 = (-1/2)(2) + 1?
                 0 = 4 - 4?                   0  =  - 1 + 1?
                    0 = 0ü                     0 = 0ü