Question

Can the following system of equations hold simultaneously?
3x+2y = 11, 2x+3y, 4x-3y = 26

Answer 1

3x+2y=11 --i
4x-3y=26 --ii
ix3
iix2
i+ii
9x+6y=33
8 x-6y=52
_________
17x=85
x=5
putting x value in equation i
15+2y=11
2y=11-15
2y=-4
y=-2

Answer 2

The given equations are :

3x + 2y = 11

2x + 3y = 4

4x - 3y = 26

let us solve the Frist two equations.

multiplying equation (1) by 2 and equation (2) by 3, we have

6x + 4y = 22
6x + 9y = 12

subtracting equation (4) from equation (5), we get

5y = -10

=> y = -2

substituting y = -2 in (4),

6x + 4 × -2 = 22

=> 6x - 8 = 22

6x = 22+8

=> 6x = 30

=> x = 30/6

=> 5

Thus, x = 5 and y = -2 is the solution of (1) and (2). putting these values of x = y in equation (3), we have

4 × 5 - 3 × -2 = 2

=> 20 + 6 = 26

=> 26 = 26

Hence, the given system of three equations can hold simultaneously and the solution is
x = 5. and y = -2

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@vaibhavhoax