Solve the simultaneous equation?

Question

2√x - 3 √y = 5
3√x + 5√y = 17

Ans: x = 16, y = 1

Please show your workings clearly..thank

Answer 1

2√x - 3√y = 5 ..... (1)
3√x + 5√y = 17 ..... (2)

Consider (1),

2√x - 3√y = 5
2√x = 3√y + 5
√x = (3√y + 5)/2 ..... (3)

Substitute (3) in (2),

3(3√y + 5)/2 + 5√y = 17
(9√y + 15 + 10√y)/2 = 17
19√y + 15 = 34
19√y = 19
√y = 1
y = 1

Put y = 1 in (3),

√x = (3 + 5)/2
√x = 4
x = 16

x = 16, y = 1 is the solution

Answer 2

2√x - 3√y = 5
3√x + 5√y = 17

Take the first equation an solve for √y then substitute it into the second equation

2√x - 3√y = 5 Add 3√y to both sides
2√x - 3√y + 3√y = 5 + 3√y
2√x = 5 +3√y Divide both sides by 2
2√x / 2 = (5 +3√y) / 2
√x = (5 + 3√y)/2

Substitute the value for √x = (5 + 3√y)/2 into the second equation

3√x + 5√y = 17
3[(5 + 3√y)/2] + 5√y = 17
3[5/2 + (3/2)√y] + 5√y = 17
3(5/2) +3(3/2)√y + 5√y = 17
15/2 +(9/2)√y + 5√y = 17 Multiply both sides by 2
15 + 9√y + 10√y = 34 Subtract 15 from both sides
19√y = 34-15
19√y = 19 Divide both sides by 19
√y =1 Square both sides
y = 1^2
y = 1 ANSWER

Substitue this value back into equation 1
2√x - 3√y = 5
2√x - 3√1 = 5
2√x - 3 = 5 Add 3 to both sides
2√x = 8 Divide both sides by 2
√x = 4 Square both sides
x = 4^2 = 16
x = 16 ANSWER

Check Answer x = 16, y = 1 put these values into equation 2
3√x + 5√y = 17
3√(16) + 5√(1) = 17
3(4) + 5 = 17
12 + 5 = 17
17 = 17 checks out

Answer 3

place the coefficients into a matrix

2 -3 | 5
3 5 | 17

eliminate numbers below pivots so

2 -3 | 5
0 19| 19

the equation in the second row shows that 19 ( root of y ) = 19 therefore y has to be 1, plug y= 1 into either equations to get the x value

Answer 4

2√x - 3 √y = 5...................(1)
3√x + 5√y = 17..................(2)

mul eq (1) by 3

6√x - 9 √y = 15

mul eq(2) by 2

6√x + 10√y = 34


6√x + 10√y = 34
-6√x + 9 √y = -15
19 √y=19
√y=1
y=1

6√x + 10√y = 34
6√x +10=34
6√x =24
√x =4
x=16

Answer 5

2√x - 3 √y = 5
3√x + 5√y = 17

let,√x=X
√y=Y
Then eqn. will be
2X - 3Y = 5 (i)
3X+ 5Y = 17 (ii)

Then frm eqn. (i)
X=5+3Y/2
then put the value of X in eqn. (ii)
Then it will be
3(5+3Y/2)+5Y = 17
then ,
15+9Y/2+5Y = 17,
then
15+9Y+10Y/2 = 17,
then
15+19Y/2 = 17
15+19Y =34
19Y = 34 - 15
19Y = 19
then
Y = 1
then put the valueof Y in eqn. (i)
then
2X - 3(1) = 5
then
2X = 8
then
X = 4
and
Y = 1
and we have
√x = X
√16 = 4
and
√y= Y
√1 = 1
we got the values
x = 16 and y = 1

Answer 6

So we have two equations:
2sqrt(x) - 3sqrt(y) = 5____(1)
3sqrt(x) + 5sqrt(y) = 17____(2)

We can write equation (2) as:
sqrt(x) = [5 + 3sqrt(y)]/2_____(3)

Substituting (3) into (2) gives:
3 {[5 + 3sqrt(y)]/2} + 5sqrt(y) = 17
Multiply both sides by 2:
3[5 + 3sqrt(y)]+ 10sqrt(y) = 34
15 + 9sqrt(y) + 10sqrt(y) = 34
19sqrt(y) = 19
sqrt(y) = 1__________(4)
Square both sides:
y = 1

Substituting (4) into (1) gives:
2sqrt(x) - 3*1 = 5
2sqrt(x) = 8
sqrt(x) = 4
Square both sides:
x = 16.

Therefore the answer is x=16, y=1.

Answer 7

is it root of x & y in the question?