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

from the second ...

y = x+3
sub into first
x^2 +x+3 = 9
x^2 + x - 6 = 0
(x+3)(x-2) = 0
x = -3 or x = 2

sub both values into y = x+3 to find their corresponding y's

Thanks

To solve the given system of equations using the substitution method, follow these steps:

Step 1: Solve one of the equations for one variable.
Let's solve the second equation, x - y + 3 = 0, for x:
x = y - 3.

Step 2: Substitute the value of the solved variable into the other equation.
Substitute x = y - 3 into the first equation, x^2 + y = 9:
(y - 3)^2 + y = 9.

Step 3: Simplify and solve the resulting equation.
Expand the square, then combine like terms:
y^2 - 6y + 9 + y = 9.
Combine like terms:
y^2 - 5y = 0.
Factor out common terms:
y(y - 5) = 0.

Now, set each factor equal to zero and solve for y:
1) y = 0.
2) y - 5 = 0 -> y = 5.

Step 4: Find the corresponding values of x for each y value.
For y = 0:
x = y - 3 = 0 - 3 = -3.
So, one solution is x = -3, y = 0.

For y = 5:
x = y - 3 = 5 - 3 = 2.
So, another solution is x = 2, y = 5.

Therefore, the solutions to the system of equations are (x, y) = (-3, 0) and (2, 5).