Question

How many solutions does this system have!

Answer 1

Answer:x=-14y=174

y=3x+5,y=-x+4

3x+5=-x+4

There are infinite number of solutions!

Move all terms containing

x

x to the left side of the equation.

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4

x

+

5

=

4

4x+5=4

y

=

−

x

+

4

y=-x+4

Move all terms not containing

x

x to the right side of the equation.

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4

x

=

−

1

4x=-1

y

=

−

x

+

4

y=-x+4

Divide each term by

4

4 and simplify.

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x

=

−

1

4

x=-14

y

=

−

x

+

4

y=-x+4

Replace all occurrences of

x

x with the solution found by solving the last equation for

x

x. In this case, the value substituted is

−

1

4

-14.

x

=

−

1

4

x=-14

y

=

−

(

−

1

4

)

+

4

y=-(-14)+4

Simplify the right side.

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x

=

−

1

4

x=-14

y

=

17

4

y=174

The solution can be shown in both point and equation forms.

Point Form:

(

−

1

4

,

17

4

)

(-14,174)

Equation Form:

x

=

−

1

4

y

=

17

4

x=-14y=174