How do you solve the following system?: 1/6x-3/5y=1 , 4/5x+2/3y = 2

2 Answers
Jul 10, 2018

x=60/19 , y= -15/19

Explanation:

Multiply the first equation by 10 => 10/6x-6y=10

Multiply the second equation by 9 => 36/5x+6y=18

Add these two equations together to give 133/15x=28

Divide by 133/15 => x=60/19

Substitute this into the first equation

=> 1/6xx60/19-3/5y=1

=> 10/19-3/5y=1

=>-3/5y=9/19

=> y= -15/19

Jul 10, 2018

x=60/19,y=-15/19

Explanation:

Solving the first equation for x:

1/6*x=1+3/5*y
so
x=6+18/5y
substituting this in the second equation:

4/5*(6+18/5y)+2/3y=2

expanding

24/5+72/25y+2/3y=2
adding -24/5

72/25y+2/3y=(10-24)/5

note that 72/25+2/3=266/75

so we get

266/75y=-14/5

multiplying by 75/266

we get y=-15/19

so x=6+18/5*(-15/19)

x=60/19