determine if the following ordered pair satisfies the system of linear equations by graphing

Question

(4,-5) 4x+y=11

4x+y=11

3x+4y=-8

Answer 1

First line 4x + y = 11

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

The equation is 4x + y  = 11

y  = - 4x + 11

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

slope = - 4 and y -intercept is 11.

y -intercept is 11, so the line crosses the y -axis at (0, 11)

Using slope find the next point.

Slope = rise/run = -4

Start at point (0, 11), move 4 unit down and 1 unit right, then plot the point (1, 7).

Draw a line through these points.

Now  the second line 3x + 4y  = - 8

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

The equation is 3x + 4y  = -8

4y  = -3x - 8

y  =  -3x /4 - 8/4

y = -3/4x - 2

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

slope = -3/4 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 = -3/4

Start at point (0, -2), move 3 units down and 4 units right, then plot the point (4,-5).

Draw a line through these points.

Graph :

From the graph we can observe the ordered pair (4 , -5) satisifies the system of linear equations.