Solve the system of equations.
2x + 6y = -18
2 = 5y - 1 (1 point)
A. (-7.25, - 1.25)
B. (4, 1)
C. (-6, - 1)
D. (5.25, 1.25)
We can solve the system of equations by using the method of substitution.
From the second equation, we can rewrite it as 5y = 3.
Dividing both sides by 5, we get y = 3/5.
Now, we can substitute y = 3/5 into the first equation:
2x + 6(3/5) = -18
2x + 18/5 = -18
Multiplying both sides by 5 to get rid of the fraction, we have:
10x + 18 = -90
Subtracting 18 from both sides, we get:
10x = -108
Dividing both sides by 10, we have:
x = -108/10 = -10.8
Therefore, the solution to the system of equations is (-10.8, 3/5).
However, none of the answer choices match this solution. Therefore, the given system of equations has no solution.
To solve the system of equations:
Step 1: Solve the second equation for y
2 = 5y - 1
Add 1 to both sides:
3 = 5y
Divide both sides by 5:
y = 3/5
Step 2: Substitute the value of y into the first equation
2x + 6(3/5) = -18
Multiply 6 by 3/5:
2x + 18/5 = -18
To eliminate the fraction, multiply both sides by 5:
10x + 18 = -90
Subtract 18 from both sides:
10x = -108
Divide both sides by 10:
x = -108/10
Simplify the fraction:
x = -54/5
So the solution to the system of equations is x = -54/5 and y = 3/5.
The answer is not one of the options provided, so none of the options is correct.
To solve the system of equations, we can use the method of substitution.
Step 1: Solve one equation for one variable.
Let's start with the second equation:
2 = 5y - 1
Add 1 to both sides:
2 + 1 = 5y
3 = 5y
Divide both sides by 5:
3/5 = y
So, we have one variable, y, solved.
Step 2: Substitute the value of y into the other equation.
Now, substitute the value of y (found in step 1) into the first equation:
2x + 6y = -18
2x + 6(3/5) = -18
Multiply 6 by 3/5:
2x + 18/5 = -18
Step 3: Solve for x.
Subtract 18/5 from both sides:
2x = -18 - 18/5
To make the denominators the same, we multiply the second term by 5/5:
2x = -90/5 - 18/5
Combine the terms:
2x = -108/5
Divide both sides by 2:
(2x)/2 = (-108/5)/2
x = -108/10
Reduce the fraction:
x = -54/5
So, the solution to the system of equations is x = -54/5 and y = 3/5.
Now, let's look at the given answer choices:
A. (-7.25, -1.25): This is not the solution we found.
B. (4, 1): This is not the solution we found.
C. (-6, -1): This is not the solution we found.
D. (5.25, 1.25): This is not the solution we found.
None of the answer choices match the solution we obtained, so none of the given options is the correct answer.