MathematicsSolve for x and y: 37x+43y=123 : 43x+37y=117.

Solve for x and y: $37 x + 43 y = 123 : 43 x + 37 y = 117$ .

A
$x = 2 and y = 1$
B
$x = 1 and y = 1$
C
$x = 1 and y = 2$
D
$x = 2 and y = 2$

Solution:

Given equations are,

37 x + 43 y = 123; 43 x + 37 y = 117

.
Multiply equation

37 x + 43 y = 123

by 43,

\Rightarrow 1591 x + 1849 y = 5289

……….(1)
Equation

43 x + 37 y = 117 by 37

,

\Rightarrow 1591 x + 1369 y = 4329

………..(2)
Subtract equation (1) by equation (2),

\Rightarrow 1591 x + 1849 y - 1591 x - 1369 y = 5289 - 4329

\Rightarrow 480 y = 960

\Rightarrow y = 2

Substitute,

y = 2

for x in the equation

43 x + 37 y = 117

.

\Rightarrow 43 x + 37 (2) = 117

\Rightarrow 43 x + 74 = 117

\Rightarrow x = 1

Thus, the value of x and y is

x = 1 and y = 2

.
Therefore, option (3) is correct.