Question

Type the correct answer in each box. Use numerals instead of words.

Consider the systems of equations below.

Answer 1

System A has 2 real solutions.

System B has 0 real solutions.

System C has 1 real solutions.

Explanation:

If the graph of system of equation intersect each other at n points then the system of equation has n real solutions.

System A:

`x^2+y^2=17` .... (1)

`y=-(1)/(2)x` .... (2)

Plot the graph of these equations.

From graph (1) it is clear that the graph of equation (1) and (2), intersect each other at two points, (-3.688,1.844) and (3.688,-1.844).

Therefore, System A has two real solutions.

System B:

`y=x^2-7x+10` .... (3)

`y=-6x+5` .... (4)

Plot the graph of these equations.

From graph (2) it is clear that the graph of equation (3) and (4), never intersect each other.

Therefore, System B has 0 real solutions.

System C:

`y=-2x^2+9` .... (5)

`8x-y=-17` .... (6)

Plot the graph of these equations.

From graph (3) it is clear that the graph of equation (5) and (6), intersect each other at one points, (-2,1).

Therefore, System C has 1 real solutions.