Chapter 4:Algebra, 4.7:Solving Simultaneous Linear Equations by Graphs

What are simultaneous equations?

Two or more equations that contain the same unknowns and must be true at the same time.

The solution is the values of the variables that satisfy both equations.

Solving by graphs

Rearrange each equation into the form y = mx + c.

Draw both equations on the same set of axes.

Each equation produces a straight-line graph.

The solution is the point where the two lines intersect.

Read the coordinates of the intersection point as (x, y).

Example

Equation 1: y = x + 1

Equation 2: y = -x + 5

Draw both lines.

They intersect at (2, 3).

Therefore, x = 2 and y = 3.

How to draw the lines

Make a table of values for each equation.

Choose several x-values.

Substitute each x-value into the equation to find y.

Plot the coordinates.

Join the points with a straight line.

The intersection

One intersection point means there is one solution.

If the lines are parallel, they never meet, so there is no solution.

If the lines are exactly the same, there are infinitely many solutions.

Accuracy

Graphical solutions may not give exact answers if the intersection is between grid lines.

A graph can be used to estimate the solution.

Algebraic methods such as substitution or elimination can give exact solutions.

Important

The coordinates of the intersection give both unknowns.

Always write the answer as x = ... and y = ....

Make sure both equations are plotted on the same axes.