USE THE GRAPHING METHOD TO TELL HOW MANY SOLUTIONS THE SYSTEM HAS:

Question

x+y=8
x+y=-1.

Answer 1

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

The first equation is x + y = 8.

Subtract x  from each side.

y = 8 - x.

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

slope = - 1 and y-intercept is 8.

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

Using slope find the next point.

Slope = rise/run = - 1/1

Start at point (0, 8), move 1 unit down and 1 unit right, then plot the point (1, 7).

The second equation is x + y = - 1.

Subtract x from each side.

 y = - 1 - x.

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

slope = - 1 and y-intercept is - 1.

y-intercept is - 1, so the line crosses the y-axis at (0, - 1)

Using slope find the next point.

Slope = rise/run = - 1/1

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

Draw the lines through these points.

Graph :

Observe the graph, the two lines are parallel lines.so,the system has no solution.