Question

Estimate the solution to the system of Equations

Answer 1

Answer letter D

Explanation:

-3x + 3y = 9

2x - 7y = -14

Let's start by simplifying both equations:

-3x + 3y = 9 (divide everything by 3)

2x - 7y = -14 (divide everything by 2)

We will then have:

-x + y = 3

x -
`(7)/(2)`y = - 7

Then we sum both equations, eliminating x and isolating y to find its value!

y + (-
`(7)/(2)`y) = 3 + (- 7)

`(2)/(2)`y + (-
`(7)/(2)`y) = - 4

Summing the fractions of y we have

-
`(5)/(2)` y = - 4 .: y =
`(8)/(5\\)` .: y = 1
`(3)/(5)`(we found y!)

Now we substitute y in one of the previous equations to find x:

-3x + 3 × (
`(8)/(5\\)` ) = 9

-3x +
`(24)/(5\\)` = 9

-3x = 9 -
`(24)/(5)`

-3x =
`(45)/(5)` -
`(24)/(5)`

-3x =
`(21)/(5)`

x =
`(21)/(5)` ÷ -3 (this is tricky, but it's the same as
`(21)/(5)` × -
`(1)/(3)` )

x = -
`(7)/(5)` .: x = - 1
`(2)/(5)`(finally found x!)

Bringing everything together we have:

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

y = 1
`(3)/(5)`

I hope it helps :)