Question

Solve the following system by substitution.
x=5y+9
x=
5
2y
.
.
.
Question content area right
Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
There are a finite number of solutions. The solution set is enter your response here.
​(Type an ordered pair. Simplify your answer. Use integers or fractions for any numbers in the​ expression.)
B.
There are infinitely many solutions. The solution set is x,enter your response here.
​(Simplify your answer. Type an expression using x as the​ variable.)
C.
The solution set is ∅.

Answer 1

To solve the system by substitution, we need to substitute the expression for x in one equation into the other equation.

Given:
x = 5y + 9

Substituting this expression for x into the equation x = 5 gives us:

5 = 5y + 9

Now we can solve this equation for y:

5y = 5 - 9
5y = -4
y = -4/5

Substitute this value of y back into the equation x = 5y + 9:

x = 5(-4/5) + 9
x = -4 + 9
x = 5

Therefore, the solution to the system is:
A. (x, y) = (5, -4/5)