Question

at which point will the graphs of the equations 2x+y=8 and x-y=4 intersect.

Answer 1

The equations are 2x + y = 8 and x - y = 4.

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

The first equation is 2x + y = 8.

y = - 2x + 8.

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

slope = - 2 and y-intercept is 8.

y-intercept is 8, so the line crosses the y-axis at (0, 8)

Using slope find the next point.

Slope = rise/run = - 2/1

Start at point (0, 8), move 2 units down and 1 unit right, then plot the point (1, 6).

The second equation is x - y = 4.

y = x - 4.

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

slope = 1 and y-intercept is - 4.

y-intercept is - 4, so the line crosses the y-axis at (0, -4).

Using slope find the next point.

Slope = rise/run = 1/1

Start at point (0, -4), move 1 unit up and 1 unit right, then plot the point (1, -3).

Draw the lines through these points.

Graph :

From the graph the two lines are intersect at (4,0).