Question

What is the solution to the system of linear equations?
2x+4y=38
10x+3y=105

Answer 1

hello :
2x+4y=38 ...(1)
10x+3y=105....(2)
-10x-20y = - 190
10x+3y =105
add : -17y = - 85
y = 5
subsct in (1) : 2x +20 =38
2x = 18
x=9

Answer 2

Answer: The required solution is (x, y) = (9, 5).

Step-by-step explanation: We are given to find the solution of the following system of linear equations :

`2x+4y=38~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\10x+3y=105~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Multiplying equation (i) by 5, we have

`5(2x+4y)=5*38\\\\\Rightarrow 10x+20y=190~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Subtracting equation (ii) from equation (iii), we get

`(10x+20y)-(10x+3y)=190-105\\\\\Rightarrow 17y=85\\\\\Rightarrow y=(85)/(17)\\\\\Rightarrow y=5.`

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

`2x+4*5=38\\\\\Rightarrow 2x+20=38\\\\\Rightarrow 2x=38-20\\\\\Rightarrow 2x=18\\\\\Rightarrow x=(18)/(2)\\\\\Rightarrow x=9.`

Thus, the required solution is (x, y) = (9, 5).