Question

solve algebraically the simultaneous equations
x^2+y^2=25 y=2x-2

Answer 1

The algebraic solutions to the system of equations are given as follows:

$(3,4), \left(-\frac{7}{5}, -\frac{24}{5}\right)$

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

• x² + y² = 25.

• y = 2x - 2.

Replacing the second equation in the first:

x² + (2x - 2)² = 25

x² + 4x² - 8x + 4 = 25

5x² - 8x - 21 = 0.

Which is a quadratic equation with coefficients a = 5, b = -8, c = -21, then:

$\Delta = (-8)^2 - 4(5)(-21) = 484$

$x_1 = \frac{-(-8) + \sqrt{484}}{2(5)} = 3$

$x_2 = \frac{-(-8) - \sqrt{484}}{2(5)} = -\frac{7}{5}$

Then, the solutions for y are:

• $y = 2(3) - 2 = 4$.

• $y = 2\left(-\frac{7}{5}\right) - 2 = -\frac{24}{5}$

Thus, the solutions are:

$(3,4), \left(-\frac{7}{5}, -\frac{24}{5}\right)$

More can be learned about a system of equations at https://brainly.com/question/24342899

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