Question

Solve the following system of equations by the substitution method.

Answer 1

Answer:  The correct option is

(B) $\left(-\dfrac{9}{2},-\dfrac{41}{2}\right).$

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

$8x=2(3x-7)+5\\\\\Rightarrow 8x=6x-14+5\\\\\Rightarrow 8x-6x=-9\\\\\Rightarrow 2x=-9\\\\\Rightarrow x=-\dfrac{9}{2}.$

From equation (iii), we get

$y=3\times\left(-\dfrac{9}{2}\right)-7\\\\\\\Rightrarow y=-\dfrac{27}{2}-7\\\\\\\Rightarrow y=-\dfrac{41}{2}.$

Thus, the required solution of the given system is $(x,y)=\left(-\dfrac{9}{2},-\dfrac{41}{2}\right).$

Option (B) is CORRECT.

Answer 2

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)