Question

Solve this system algebraically.

7x - 2y = 4 5y + 3x = 10

{(-41/40, -41/58)}
{(41/40, 41/58)}
{(-40/41, -58/41)}
{(40/41, 58/41)}

Answer 1

The answer for this question is the last option which is D.

Answer 2

Answer: The correct option is

(D)
`(x,y)=\left((40)/(41),(58)/(41)\right).`

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

`7x-2y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\5y+3x=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Multiplying equation (i) by 5, we have

`5(7x-2y)==4* 5\\\\\Rightarrow 35x-10y=20~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Multiplying equation (ii) by 2, we have

`2(5y+3x)=2* 10\\\\\Rightarrow 10y+6x=20~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Adding equations (iii) and (iv), we get

`35x+6x=20+20\\\\\Rightarrow 41x=40\\\\\Rightarrow x=(40)/(41).`

Substituting the value of x in equation (ii), we get

`5y+3*(40)/(41)=10\\\\\Rightarrow 5y+(120)/(41)=10\\\\\Rightarrow 5y=10-(120)/(41)\\\\\Rightarrow 5y=(290)/(41)\\\\\Rightarrow y=(290)/(205)\\\\\Rightarrow y=(58)/(41).`

Thus, the required solution is

`(x,y)=\left((40)/(41),(58)/(41)\right).`

Option (D) is correct.