Solve the simultaneous equations
y = 3 – 2x
x2 + y2 = 18
Show clear algebraic working.

(

x

,

y

)

=

(

3

5

,

4

1

5

)

or

(

x

,

y

)

=

(

−

3

,

−

3

)

Explanation:

Given

[1]

XXX

y

−

2

x

=

3

[2]

XXX

x

2

+

y

2

=

18

Re-writing [1]

[3]

XXX

y

=

2

x

+

3

Substituting

(

2

x

+

3

)

from [3] for

y

in [2]

[4]

XXX

x

2

+

(

2

x

+

3

)

2

=

18

Simplifying

[5]

XXX

x

2

+

4

x

2

+

12

x

+

9

=

18

[6]

XXX

5

x

2

+

12

x

−

9

=

0

Factoring

[7]

XXX

(

5

x

−

3

)

(

x

+

3

)

=

0

⇒

x

=

3

5

or

x

=

−

3

case 1:

x

=

3

5

Substituting

3

5

for

x

in [3]

XXX

y

=

2

(

3

5

)

+

3

=

4

1

5

case 2:

x

=

−

3

Substituting

(

−

3

)

for

x

in [3]

XXX

y

=

2

(

−

3

)

+

3

=

−

3