Question

Hich ordered pair is the solution to the system of equations? {x=(1)/(2)y+5} {2x+3y=-14}

Answer 1

(2, - 6 )

Explanation:

Given the 2 equations

x =
`(1)/(2)` y + 5 → (1)

2x + 3y = - 14 → (2)

Substitute x =
`(1)/(2)` y + 5 into (2)

2(
`(1)/(2)` y + 5 ) + 3y = - 14 ← distribute and simplify left side

y + 10 + 3y = - 14

4y + 10 = - 14 ( subtract 10 from both sides )

4y = - 24 ( divide both sides by 4 )

y = - 6

Substitute y = - 6 into (1) for corresponding value of x

x = (0.5 × - 6 ) + 5 = - 3 + 5 = 2

Solution is (2, - 6 )

Answer 2

The solution to the system of equations is (2,-6).

Explanation:

Given : Equations
`x=(1)/(2)y+5` and
`2x+3y=-14`

To find : Which ordered pair is the solution to the system of equations?

Solution :

Write the equation
`x=(1)/(2)y+5` as
`2x=y+10` ....(1)

Let
`2x+3y=-14` ....(2)

Substitute the value of '2x' from (1) in (2),

`y+10+3y=-14`

`4y=-24`

`y=(-24)/(4)`

`y=-6`

Substitute in
`x=(1)/(2)y+5` ,

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

`x=-3+5`

`x=2`

The solution to the system of equations is (2,-6).