Question

Solve the following system of equations.

y = x - 1
x^2 + y^2 =25

A) (-3,-4) (4,3)

B) (4,3)

C) (-3,-4)

D) No solution

Answer 1

The answer is option A

Once you try substituting the values of options B and C, the equation is equal on both left and right hand sides hence the solutions is A

Answer 2

Option A

A) (-3,-4) (4,3)

Explanation:

We have a system of equations composed of:

The equation of a circle that has center at point (0,0) and radius r = 5.

The equation of a line that intercepts the y-axis at point (0,1)

To solve the system we substitute the equation of the line in the equation of the circumference:

`y = x - 1\\\\x ^ 2 + y ^ 2 = 25`

Then

`x ^ 2 + (x-1) ^ 2 = 25`

We solve for x.

`x ^ 2 + x ^ 2 -2x +1 = 25\\\\2x ^ 2 -2x -24 = 0`

We divide by 2 both sides of the equation

`x^2 -x -12 = 0`

We look for two numbers that multiply as a result -12 and that add them as a result -1.

These numbers are -4 and 3.

Therefore the factors are:

`(x-4) (x + 3) = 0`

Finally the solutions are:

`x = 4` and
`x = -3`

The ordered pairs are:

(-3,-4) (4,3)