Question

solve graphically
2x + y =8
x+y=5​

Answer 1

Answer:

This could be solved with either elimination or substitution. I'll use elimination, since the category is "Linear Systems with Multiplication."

Multiply the first equation by

−

1

.

−

1

(

x

+

y

=

5

)

→

−

x

−

y

=

−

5

We now have the two equations:

{

−

x

−

y

=

−

5

2

x

+

y

=

8

Add the two equations together.

−

x

+

2

x

−

y

+

y

=

−

5

+

8

Simplify. Notice that the

y

terms cancel, which was the point in multiplying the first equation by

−

1

earlier.

x

=

3

Now, substitute

x

=

3

into either of the original equations.

3

+

y

=

5

y

=

2

This leaves us with

x

=

3

,

y

=

2

, or the point

(

3

,

2

)

.