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

$5(2x+4y)=5\times38\\\\\Rightarrow 10x+20y=190~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

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

$(10x+20y)-(10x+3y)=190-105\\\\\Rightarrow 17y=85\\\\\Rightarrow y=\dfrac{85}{17}\\\\\Rightarrow y=5.$

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

$2x+4\times5=38\\\\\Rightarrow 2x+20=38\\\\\Rightarrow 2x=38-20\\\\\Rightarrow 2x=18\\\\\Rightarrow x=\dfrac{18}{2}\\\\\Rightarrow x=9.$

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