Question

Is the answer a, b, c, or d.

Answer 1

The correct answer is d.

We have the following system of linear equations:

(I)
`4x+7y=-14`
(II)
`8x+5y=8`

Let's use the elimination method, then let's multiply the equation (1)
`*(-2)` and subtracting (I) and (II):

(I)
`-2(4x+7y)=-2(-14)`
∴
`-8x-14y=28`

(I)
`-8x-14y=28`
(II)
`8x+5y=8`
____________________
(III)
`-9y=36`

∴
`y=-4`

We can find the value of x by substituting y either in (I) or (II). Thus, from (I):


`4x+7(-4)=-14`
∴
`4x-28=-14`
∴
`4x=14`
∴
`x=(14)/(4)`
∴
`\boxed{x=(7)/(2)}`

Let's substitute the values of x and y into (I) and (2)

(I)
`4((7)/(2))+7(-4)=14-28=-14`
(II)
`8((7)/(2))+5(-4)=28-20=8`

Finally the answer is:


`\boxed{x=(7)/(2) \rightarrow x= 3 (1)/(2)}`