Question

Y2 + x2 = 53
y − x = 5

Answer 1

To solve the given system of equations, we can use the substitution method. By substituting one equation into another, we can find the values of x and y that satisfy both equations. The solution to the system of equations is x = 2 and y = 7, or x = -7 and y = -2.

Step-by-step explanation:

The given system of equations is:

y2 + x2 = 53

y - x = 5

To solve this system, we can use substitution or elimination method. Let's use substitution:

1. From the second equation, we can solve for y: y = x + 5
2. Substitute y in the first equation with x + 5: (x + 5)2 + x2 = 53
3. Expand and simplify the equation: x2 + 10x + 25 + x2 = 53
4. Combine like terms: 2x2 + 10x + 25 - 53 = 0
5. Simplify the equation: 2x2 + 10x - 28 = 0
6. Factor the equation: 2(x - 2)(x + 7) = 0
7. Solve for x: x - 2 = 0 or x + 7 = 0
8. If x - 2 = 0, then x = 2. If x + 7 = 0, then x = -7.
9. Substitute the values of x back into y = x + 5 to find y: y = 2 + 5 or y = -7 + 5
10. If x = 2, then y = 7. If x = -7, then y = -2.

Therefore, the solution to the system of equations is x = 2 and y = 7, or x = -7 and y = -2.

Answer 2

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