Question

The graphs of the functions g(x) = 6x + a and h(x) = 2x + b, where a and b are constants, are shown. They intersect at the point (p,q).

A. Label the graphs as "g" and "h".
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Answer 1

A labelled graph of the solution to the system of two functions is shown in the image below.

In order to graphically determine the solution for this system of linear equations on a coordinate plane, we would make use of an online graphing calculator to plot the given system of linear equations while taking note of the point of intersection;

g(x) = 6x + a ......equation 1.

h(x) = 2x + b ......equation 2.

where:

• a is equal to 3.
• b is equal to 8.

Based on the graph shown, we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph that represents them in quadrant I. Hence, this is represented by the ordered pair (1.25, 10.5).

In this context, the pair of linear equation has exactly one solution;

x = 1.25

y = 10.5