Question

Find the solution to the system

Answer 1

The solution of the system of equations; $y = \frac{1}{2}\cdot x - 1$ and x = 4, represented on the graph is the point (4, 1)

Where on a graph is the solution of the equations of two straight lines on the graph?

The graphs are straight line graphs that can be represented with linear functions.

The points on the graph with blue line are; (2, 0), (0, -1)

The slope, m, is therefore;

m = (0 - (-1))/(2 - 0) = 0.5

From the point, (2, 0), we have;

y = 0.5•(x - 2) = 0.5•x - 1

y = 0.5•x - 1...(1)

$y = \frac{1}{2}\cdot x - 1$

The equation of the graph that is constructed with red line is x = 4...(2)

The solution is given by equation (1) when x = 4 as follows;

• On the blue line, y = 0.5•x - 1
• On the red line, x = 4

The solution satisfies both lines, and it is the point of intersection. At the solution, therefore;

y = 0.5•x - 1 and x = 4

Which gives;

y = 0.5 × 4 - 1 = 1

At the solution, x = 4, and y = 1, which gives the point, (4, 1)

Learn more about linear functions here:

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