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Simultaneous linear equation in two variables, analytical and graphical solutions. Simultaneous linear in equations. Practical problems on linear equations.

The values of x and y that simultaneously  satisfy the equations 2x + 3y = 5 and 7x - 4y = 3 are :

Option:
A. 0, 1
B. 1, 0
C. -1, 1
D. 1, 1
Answer: D . 1, 1

Justification:

Equation I = 2x + 3y = 5
Equation II = 7x - 4y = 3

Multiplying first equation by 4 =
-> 2x + 3y = 5
.`. (2x + 3y = 5) x (4)
= (8x + 12y = 20)......... (equation.III)

Now Multiplying second equation by 3 =
-> 7x - 4y = 3
.`. (7x - 4y = 3) x (3)
= (21x - 12y = 9).......... (equation IV)

Now, Add Equation III  with Equation IV.
-> (8x + 12y = 20) + (21x - 12y = 9)
-> (8x + 21x) + (12y - 12y) = (20 + 9)
-> 29x + 0 = 29
-> 29x = 29
-> x = 29/29
-> x = 1
We get : x = 1,
Now Putting x = 1 in Equation I,
-> 2x + 3y = 5
-> 2(1) + 3y = 5
-> 2 + 3y = 5
-> 3y = 5 - 2
-> 3y = 3
-> y = 3/3
-> y = 1

So (x, y) = (1, 1)

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