x^2+y=9, x-y+3=0. Need to solve using substitution method.

To solve the system of equations using the substitution method, we'll solve one equation for one variable and substitute that expression into the other equation. Let's solve the second equation for x:

x - y + 3 = 0

Rearrange the equation to express x in terms of y:

x = y - 3

Now substitute this expression for x into the first equation:

x^2 + y = 9

(y - 3)^2 + y = 9

Expand and simplify the equation:

y^2 - 6y + 9 + y = 9

Combine like terms:

y^2 - 5y = 0

Now factor out the common term y:

y(y - 5) = 0

Set each factor equal to zero and solve for y:

1) y = 0

2) y - 5 = 0
y = 5

Now that we have the y-values, we can substitute them back into the expression we found for x.
For y = 0

x = y - 3
= 0 - 3
= -3

So one solution is x = -3 and y = 0.

For y = 5

x = y - 3
= 5 - 3
= 2

The other solution is x = 2 and y = 5.

Therefore, the system of equations has two solutions: (-3, 0) and (2, 5).