2x-y=0 and 4x-y=2

Question

solve the following system of equations graphically.

Answer 1

The first line equation is 2x - y = 0.

Write the equation in slope - intercept form y = mx + b, where m is slope and b is y - intercept.

y = 2x.

Compare the equation with slope - intercept form y = mx + b.

slope = 2 and y - intercept is 0.

y - intercept is 0, so the line crosses the y - axis at origin (0, 0).

Using slope find the next point.

Slope = rise/run = 2/1

Start at point (0, 0), move 2 units up and 1 unit right, then plot the point (1, 2).

Draw a line through these points.

The second line equation is 4x - y  = 2.

Write the equation in slope - intercept form y = mx + b, where m is slope and b is y - intercept.

y = 4x - 2.

Compare the equation with slope - intercept form y = mx + b.

slope = 4 and y -intercept is - 2.

y - intercept is - 2, so the line crosses the y - axis at (0, - 2).

Using slope find the next point.

Slope = rise/run = 4/1

Start at point (0, - 2), move 4 units up and 1 unit right, then plot the point (1, 2).

Draw a line through these points.

Graph :

From the graph lines are intersecting at (1, 2).

So, the solution of the given system is x = 1 and y = 2.