How do you solve the system of equations 2x+8y=6 and -5x-20y=-15?

2 Answers
Nov 19, 2016

This system of equation doesn't have any solutions.

Explanation:

2x+8y=6
-5x-20y=-15

Let's simplify these equations: divide the first one by 2 andd the second by -5:

x+4y=3
x+4y=15

Now, using any of the equations, we must express one variable by the other, let's say x by y from the second equation:

x=15-4y

Using this we solve the other equation:

x+4y=3
15-4y+4y=3
15=3

We got 15=3 which obviously isn't true so this equation has no solution. It follows that this system of equation doesn't have any solutions as well.

Nov 19, 2016

x can have any value and the equations will work.
The y- values will depend on the x chosen.

Explanation:

2x+8y =6" and "-5x -20y = -15

There are different options available to solve the equations.
rarr" " elimination
rarr" " substitution rarr single variable
rarr" " equating
rarr" "matrices
rarr" " graphically

To be able to use substitution, a single variable in one of the equations is a useful indicator

2x+8y =6 " "div2 rarr " "x+4y=3

Make x the subject of the equation:

color(red)(x = 3-4y)

Replace color(red)x in the second equation by color(red)((3-4y))

" "-5color(red)(x) -20y = -15
color(white)(xxxx)darr
-5color(red)((3-4y))-20y =-15

-15+20y -20y = -15

-15 = -15

x can have any value