Question

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

Answer 1

Answer:

(2, - 6 )

Step-by-step explanation:

Given the 2 equations

x = $\frac{1}{2}$ y + 5 → (1)

2x + 3y = - 14 → (2)

Substitute x = $\frac{1}{2}$ y + 5 into (2)

2( $\frac{1}{2}$ 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

Answer:

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

Step-by-step explanation:

Given : Equations $x=\frac{1}{2}y+5$ and $2x+3y=-14$

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

Solution :

Write the equation  $x=\frac{1}{2}y+5$  as  $2x=y+10$ ....(1)

Let  $2x+3y=-14$  ....(2)

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

$y+10+3y=-14$

$4y=-24$

$y=\frac{-24}{4}$

$y=-6$

Substitute in $x=\frac{1}{2}y+5$ ,

$x=\frac{1}{2}(-6)+5$

$x=-3+5$

$x=2$

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