Question

Type the correct answer in each box. Use numerals instead of words.
Consider the systems of equations below.
System A
System B
1² + y² = 17
y = 1² - 71 + 10
y = -6x + 5
Determine the number of real solutions for each system of equations.
System A has
real solutions.
System B has
real solutions.
System Chas
real solutions.
System C
= -21² + 9
8r - y = -17

Answer 1

From the system of equations given, it is correct to state that:

• System A has two real solutions
• System B has two real solutions
• System C has one real solution.

What are system of equations?

System of equations refers to a matrix that has elements which are representative of the coefficients of the given equations.

What are the solutions to the above systems of equations?

System A:
x² + y² = 17

y = -1/2x

The two real solutions to the above system is given as:

$x = -2 \sqrt {(17/5)},y = \sqrt{(17/5)}$ and
$x = 2 \sqrt{(17/5)} , y = -\sqrt{(17/5)}$

System B:
y = x² - 7x + 10
y = -6x +5

The two real solutions to the above system is given as:

${x = 1/2 (1 - i \sqrt{(19)} ), y = 2 + 3 i \sqrt{(19)}$

${x = 1/2 (1 + i \sqrt{(19)} ), y = 2 - 3 i \sqrt{(19)}$

System C
y = -2x² + 9

8x-y = -17

The one real solution is given as:

x = -2, y = 1

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