Question

Graph this system of equations. 1.15x + 0.65y = 8.90 x − 3y = -15

Answer 1

Answer:

We have the equations:

1.15x + 0.65y = 8.90

and

x − 3y = -15

First, let's write them in the slope-intercept form:

The first one will be:

y = -(1.15/0.65)*x + 8.90/0.65  

The second:

y = (1/3)*x + 15/3 = (1/3)*x + 5.

then our system is:

y = -(1.15/0.65)*x + 8.90/0.65  

y  = (1/3)*x + 5.

To graph each line, you can just evaluate the line in two points (for x = 0 and x = 1, for example) and then locate those points in the coordinate axis, and then draw a line that connects them.

For example with the second line:

y(0) = (1/3)*0 + 5 = 5

then we have the point (0,5)

and

y(3) = (1/3)*3 + 5 = 8

Then we have the point (3,8)

With the first equation may be a little harder, as the coefficients are not whole numbers, we can rewrite it as:

y = (1.15/0.65)*x + 8.90/0.65  = (115/65)*x + (890/65)

Where i multiplied and divided by 100 the numerators and denominators in the right side, so now is easier to work with it.

The points you can use are:

y(0) =  (115/65)*0 + (890/65) = 13.7

the point is (0, 13.7)

and:

y(1) = (115/65)*1 + (890/65) = 15.5

The point is (1, 15.5)

Below you can see the graphs of both functions:

blue: y = -(1.15/0.65)*x + 8.90/0.65

red: y  = (1/3)*x + 5