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 ∅.
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)
To solve the system of equations by substitution, we will first solve one equation for one variable and then substitute that expression into the other equation.
Given system of equations:
1) x = 5y + 9
2) x = 2y
Since both equations are already solved for x, we can set them equal to each other:
5y + 9 = 2y
Then, we can solve for y:
5y - 2y = -9
3y = -9
y = -9/3
y = -3
Now that we have found the value of y, we can substitute it back into either equation to find the value of x. Let's use equation 2):
x = 2y
x = 2(-3)
x = -6
Therefore, the solution to the system of equations is the ordered pair (-6, -3).
Since there is a finite number of solutions, the correct choice is:
A. There are a finite number of solutions. The solution set is (-6, -3).
To solve the given system of equations by substitution, we will solve one of the equations for one variable and substitute it into the other equation. Let's solve the first equation, x = 5y + 9, for x.
Step 1: Solve for x in terms of y
x = 5y + 9
Step 2: Substitute the value of x into the second equation
x = 5
5 = 5y + 9
Step 3: Solve the equation for y
5y + 9 = 5
Subtract 9 from both sides
5y = -4
Divide both sides by 5
y = -4/5
Step 4: Substitute the value of y back into the first equation to get x
x = 5y + 9
x = 5(-4/5) + 9
x = -4 + 9
x = 5
Therefore, the solution to the system of equations is (x, y) = (5, -4/5).
Now, let's determine the correct choice:
A. There are a finite number of solutions. The solution set is (5, -4/5).
B. There are infinitely many solutions. The solution set is x = 5.
C. The solution set is ∅.
Based on the calculations, we have determined that the correct choice is A.