Solving Linear Equations Graphically
To solve a linear equation graphically,
- Write two functions using each expression in the equation
as a rule.
- Graph both functions on the same coordinate plane.
- Determine the point of intersection.
The solution of the equation is the x -coordinate of the point
The y -coordinate is the value obtained for both expressions
when the equation is evaluated with the solution.
2x + 3 = x + 5
1. y1 = 2 x + 3; y 2 =
x + 5
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:
- One solution exists when the graphs intersect.
- No solution exists when the graphs are parallel.
- An infinite number of solutions exist when the graphs