Question

Consider the systems of equations below.

System A
12+y 2 =17
8x−y=−17

Determine the number of real solutions for each system of equations.

System A has:
a. 0 real solutions.
b. 1 real solution.
c. 2 real solutions.
d. Infinite real solutions.

Answer 1

System A, which consists of the equations 1) 12+y^2=17 and 2) 8x-y=-17, has two real solutions. This is determined by finding the two possible values of y from the first equation and then substituting these into the second equation to solve for x.

Step-by-step explanation:

The student's question is asking about the number of real solutions for system A, which comprises the equations 1) 12+y^2=17 and 2) 8x-y=-17. To find the number of real solutions, we first solve each equation separately.

For equation 1): By subtracting 12 from both sides, we get y^2=5. Taking the square root of both sides, we have y=±√5, which gives us two possible values for y.

For equation 2): Adding y to both sides and then dividing by 8, we get x= (y+17)/8. Because the first equation gives us two values for y, we can substitute these into the second equation and find respective values of x, resulting in two pairs of (x, y) that satisfy the system. Thus, system A has c. 2 real solutions.