Question

Solve the system of linear equations:16x+17y=1 12x−15y=1 x= y=

Answer 1

We will use the elimination method to solve that system:

Let's look at the denominators of the coefficients for the x variable, in this case we have 2 and 6, lets convert the second equation to have 1/6 as coefficient, so:

`(1)/(2)x-(1)/(5)y=1`
`(1)/(2)x\cdot(1)/(3)-(1)/(5)y\cdot(1)/(3)=1\cdot(1)/(3)`
`(1)/(6)x-(1)/(15)y=(1)/(3)`

We already have the same coefficient, now we are going to subtract:

`(22)/(105)y=(2)/(3)`
`y=(105\cdot2)/(22\cdot3)`
`y=(210)/(66)=(105)/(33)=(35)/(11)`

We already have the value of y, now we can find the value of x by substituting in any of the equations, let's use the second one:

`(1)/(2)x-(1)/(5)y=1`
`(1)/(2)x-(1)/(5)\cdot(35)/(11)=1`
`(1)/(2)x-(35)/(55)=1`
`(1)/(2)x-(7)/(11)=1`
`(1)/(2)x=1+(7)/(11)`
`(1)/(2)x=(18)/(11)`
`x=(18\cdot2)/(11)`
`x=(36)/(11)`