Question

Solve the following system of equations by the substitution method.

8x = 2y + 5
3x = y + 7

What is the solution set?

{(-41/2, -9/2)}
{(-9/2, -41/2)}
∅

Answer 1

Let

Eqn 1 be 8x = 2y + 5

And,

3x = y + 7
therefore

Eqn 2 is x= 1/3(y+7)

Sub 2 into 1 gives:

8(1/3(y+7)) = 2y + 5

8/3(y) + 56/3 = 2y + 5

2/3(y) = –41/3
2y=–41
y= –41/2

X= –9/2.

Therefore, {(-9/2, -41/2)} is your solution set. As the notation is equal to (x,y)

Answer 2

Answer: The correct option is

(B)
`\left(-(9)/(2),-(41)/(2)\right).`

Step-by-step explanation: We are given to solve the following system of equations by the substitution method :

`8x=2y+5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x=y+7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

From equation (ii), we have

`3x=y+7\\\\\Rightarrow y=3x-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Substituting the value of y from equation (iii) in equation (i), we get

`8x=2(3x-7)+5\\\\\Rightarrow 8x=6x-14+5\\\\\Rightarrow 8x-6x=-9\\\\\Rightarrow 2x=-9\\\\\Rightarrow x=-(9)/(2).`

From equation (iii), we get

`y=3*\left(-(9)/(2)\right)-7\\\\\\\Rightrarow y=-(27)/(2)-7\\\\\\\Rightarrow y=-(41)/(2).`

Thus, the required solution of the given system is
`(x,y)=\left(-(9)/(2),-(41)/(2)\right).`

Option (B) is CORRECT.