Question

b) Use a graphical method to find
estimates for the solutions of the
simultaneous equations
x² + y² = 2.25
y - x = 1​

Answer 1

Answer:

First add

x

to both sides of the second equation to get:

y

=

x

+

3

Then substitute this expression for

y

into the first equation to get:

29

=

x

2

+

(

x

+

3

)

2

=

2

x

2

+

6

x

+

9

Subtract

29

from both ends to get:

0

=

2

x

2

+

6

x

−

20

Divide both sides by

2

to get:

0

=

x

2

+

3

x

−

10

=

(

x

+

5

)

(

x

−

2

)

So

x

=

2

or

x

=

−

5

If

x

=

2

then

y

=

x

+

3

=

5

.

If

x

=

−

5

then

y

=

x

+

3

=

−

2

So the two solutions

(

x

,

y

)

are

(

2

,

5

)

and

(

−

5

,

−

2

)

Step-by-step explanation:

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