Question

Use the substitution method to solve
x^2+2y^2=9
x-y+3=0
can someone show me the steps?

Answer 1

I know the answer is x=1 and y=2 just let me get you the steps

Answer 2

okay let's call the equations (1) and (2) respectively
solve (2) for y, you can easily get:
y=x+3 (3)
now substitute the for y in equation (1):
\[x^2+2(x+3)^2=9 \implies x^2+2(x^2+6x+9)=9\]
\[x^2+2x^2+12x+18=9 \implies 3x^2+12x+9=0\]
divide by 3 for simplification and factorize the expression
\[x^2+4x+3=0 \implies (x+1)(x+3)=0\]
\[x=-1 , x=-3\]
substitute in equation (3) to get the correspondent values of y to each value of x