Question

Find the value
of x and y
if 3x + 2y = 11 and 2x + 3y = 4​

Answer 1

Answer:

Y= -2

X= 5

Step-by-step explanation:

3x+2y=11 ----------(1)

2x+3y=4-------------(2)

Multiplying (1) with 2, to make the coefficients of x equal to both the equations

6x+4y=22------------(3)

Multiplying (2) with 3, to make the coefficients of x equal to both the equations.

6x+9y=12-----------(4)

Now, Since, the coefficients of x of both equations are equal and have the same sign, we can eliminate it, by subtracting (3) from(4)

6x+9y=12

-(6x+4y=22)

5y= -10

y= -2---------(5)

Now taking (5) in (1)

3x+2×-2=11

3x-4=11

3x= 15

x= 15/3= 5

Answer 2

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3x + 2y = 11 ------ (1)

2x + 3y = 4 ------- (2)

From (1) we get :-

y = $\frac{11-3x}{2}$ ------ (3)

Putting (3) in (2) we get :-

2x + 3y = 4

2x + 3 × $\frac{11-3x}{2}$ = 4

2x + $\frac{33-9x}{2}$ = 4

$\frac{4x + 33 - 9x}{2}$ = 4

4x - 9x + 33 = 4 × 2

33 - 5x = 8

33 - 8 = 5x

25 = 5x

x = $\frac{25}{5}$

x = $\frac{\cancel{25}}{\cancel{5}}$

x = 5 -------- (4)

Putting value of (4) in (1)

3x + 2y = 11

3 × 5 + 2y = 11

15 + 2y = 11

2y = 11 - 15

2y = (-4)

y = $\frac{(-4)}{2}$

y = $\frac{\cancel{(-4)}}{\cancel{2}}$

y = (-2)

∴ Value of x = 5 and y = (-2)