May 25th

May 25th

Solving Linear Equations Graphically

To solve a linear equation graphically,

1. Write two functions using each expression in the equation as a rule.
2. Graph both functions on the same coordinate plane.
3. Determine the point of intersection.

The solution of the equation is the x -coordinate of the point of intersection.

The y -coordinate is the value obtained for both expressions when the equation is evaluated with the solution.

Example:

2x + 3 = x + 5

1. y₁ = 2 x + 3; y ₂ = x + 5

2.

3. (2, 7); solution is 2

Try the following:

1) 3x + 5 = 2x

2) 6x - (4x + 3) = 7 - 3x

There are three possibilities when solving linear equations:

1. One solution exists when the graphs intersect.
2. No solution exists when the graphs are parallel.
3. An infinite number of solutions exist when the graphs coincide.