Question

If x²–y² = 135 and x–y = 9, find the values of x and y​

Answer 1

(x-y) = 135

Squaring both sides,

(x-y)^2 = 18,225

x^2 + y^2 - 2xy = 18,225

x^2 + y^2 = 18,225 + 2xy = 18,225+2*9 = 18,225+18 = 18,243.

Hope this helps you!

Answer 2

Answer: x = 12 and y = 3

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Step-by-step explanation:

x^2 - y^2 = 135

(x-y)(x+y) = 135 ... difference of squares rule

9(x+y) = 135 ... replace x-y with 9

x+y = 135/9

x+y = 15

We have this system of equations now

`\begin{cases}x+y = 15\\x-y = 9\end{cases}`

Add the equations straight down

• x+x = 2x
• y+(-y) = 0y = 0 which means the y term goes away
• 15+9 = 24

We end up with 2x = 24 which solves to x = 12.

Then use x = 12 in any of the equations with x & y in it to find that y = 3

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Check:

x^2-y^2 = 135

12^2 - 3^2 = 135

144 - 9 = 135

135 = 135

The first equation is confirmed.

x-y = 9

12-3 = 9

9 = 9

Both equations are confirmed.