Graph -5x + y =5 and -x + y =5 on the same axis

Question

Graph both equasions on the same set of axis then reading the solution of the graph.

-5x + y =5

-x + y =5

Answer 1

Given equation is -5x+y = 5

Add 5x to each side.

-5x+5x+y = 5+5x

y = 5x+5

And -x+y = 5

Add x to each side.

-x+x+y = 5+x

y = x+5

Graph of the equations -5x+y = 5 and -x+y = 5.

Observe the graph the two lines are intersecting.

Intersecting point is (0,5).

Above coordinate pair is represents x.y.

Solution x = 0, y = 5.

 

Answer 2

The equations are - 5x + y = 5 and - x + y = 5

• First line - 5x + y = 5

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

The equation is - 5x + y = 5

y = 5x + 5

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

slope = 5 and y -intercept is 5.

y -intercept is 5, so the line crosses the y -axis at (0, 5)

Using slope find the next point.

Slope = rise/run = 5/1

Start at point (0, 5), move 5 units up and 1 unit right, then plot the point (1, 10).

Draw a line through these points.

• Second line - x + y = 5

y = x + 5

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

slope = 1 and y-intercept is 5.

y -intercept is 5, so the line crosses the y -axis at (0, 5)

Using slope find the next point.

Slope = rise/run = 1/1

Start at point (0, 5), move 1 units up and 1 unit right, then plot the point (1, 6).

Draw a line through these points.

Graph

From the graph we observe the two lines are intersecting at (0, 5).

Solution: x = 0 and y = 5.