Question

Graph the system of equations
4x+4y=16
x+6y=-6

Answer 1

Graph has been shown in the attached file.

Explanation:

We have been given the system of equations

`4x+4y=16.......(1)\\x+6y=-6.........(2)`

Both the equation represents a straight lines. We can find the x and y intercepts of these lines to graph.

The intercept form of a line is given by

`(x)/(a)+(y)/(b)=1`

Here a is the x - intercept and b is the y-intercept.

Divide both sides of the equation (1) by 16

`(4x)/(16)+(4y)/(16)=1\\\\(x)/(4)+(y)/(4)=1`

Hence, x-intercept = 4 and the point is (4,0)

y-intercept = 4 and the point is (0,4)

Similarly, for the second line

Divide both sides of the equation (2) by -6

`(x)/(-6)+(6y)/(-6)=1\\\\(x)/(-6)+(y)/(-1)=1`

x-intercept = -6 and the point is (-6,0)

y-intercept = -1 and the point is (0,-1)

We'll plot these points in the xy- plane and then join to get the graph of these lines.