Question

Solve the following systems algebraically.
3.
[y+ x = 17
x² + y² = 169

Answer 1

To solve the system of equations, we use the method of substitution to find the values of x and y that satisfy both equations. The solutions to the system are (4, 13) and (15, 2).

Step-by-step explanation:

To solve the system of equations algebraically, we can use the method of substitution.

Solution:

1. From the first equation, we can isolate y by subtracting x from both sides: y = 17 - x
2. Substitute this value of y into the second equation: x^2 + (17 - x)^2 = 169
3. Expand and solve the resulting quadratic equation: x^2 + x^2 - 34x + 289 = 169
4. Combine like terms and rearrange the equation to standard form: 2x^2 - 34x + 120 = 0
5. Factor the quadratic equation: (x - 4)(2x - 30) = 0
6. Solve for x: x = 4 or x = 15
7. Plug these values back into the first equation to find the corresponding values of y: For x = 4, y = 17 - 4 = 13; For x = 15, y = 17 - 15 = 2
8. The solutions to the system of equations are (x, y) = (4, 13) and (15, 2).

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