Question

Directions: Use system of linear equations

9x-3y=-1

1/5x+2/5y=-1/3

Answer 1

The solution to this set of linear equations is:

`x=-(1)/(3)\\y=-(2)/(3)`

Step-by-step explanation:

This is a system of two equations with two unknown variables x and y, let's call them

Equation 1:
`9x-3y=-1`

Equation 2:
`(1)/(5)x+(2)/(5)y=-(1)/(3)`

The first step is to solve Equation 1 for y, this means to leave the y alone on one side of the equal

`y= 3x+(1)/(3)`

Then with this equation, you can find the value of x by replacing y in Equation 2

`(1)/(5)x+(2)/(5)(3x+(1)/(3))=-(1)/(3)`

Then simplify this equation to find x

`(1)/(5)x+(6)/(5)x+(2)/(15)=-(1)/(3)`

`(1)/(5)x+(6)/(5)x=-(1)/(3)-(2)/(15)`

`(7)/(5)x=-(5)/(15)-(2)/(15)`

`(7)/(5)x=-(7)/(15)`

Now you solve for x

`x=-(1)/(3)`

Now you use this value of x to find y

`y=3(-(1)/(3))+(1)/(3)\\y=-(2)/(3)`

You can check if this answer is correct by replacing the values of x and y into Equation 1 or 2, in this case, let's take Equation 1:

`9(-(1)/(3))-3(-(2)/(3))=-1\\-3+2=-1\\-1=-1\\`