Solve the following system by the substitution method x y

Solve the following system by the substitution method. x + y = 5 y = x^2 - 7 Select the correct choice below and, if necessary, fill in the answer box to The solution set is {}. (Type an ordered pair. Use a comma to separate answers as needed. There is no solution.

Solution

Given x+y=5 and y=x²-7

From x+y=5

y=5-x

Substitute y=5-x in y=x²-7

y=x²-7

5-x=x²-7

x²-7-5+x=0

x²+x-12=0

(x+4)(x-3)=0

x+4=0 or x-3=0

x=-4 x=3

Therefore,x=-4,3

Substitute x=-4 in y=5-x

y=5-(-4)=5+4=9

Substitute x=3 in y=5-x

y=5-3=2

When x=-4,y=9

When x=3,y=2

Therefore, the solution set is {(3,2),(-4,9)}

The Option A is the correct one.