Solve the system of equations.
2x + 6y = -18
2 = 5y - 1
A. (-7.25, - 1.25)
B. (4, 1)
C. (-6, - 1)
D. (5.25, 1.25)
To solve this system of equations, we can solve one equation for either variable and substitute it into the other equation.
First, let's solve the second equation for y:
2 = 5y - 1
Adding 1 to both sides, we get:
3 = 5y
Dividing both sides by 5, we get:
y = 3/5
Now, substitute this value of y into the first equation:
2x + 6(3/5) = -18
Multiply 6 by 3/5:
2x + 18/5 = -18
Multiply both sides by 5 to eliminate the fraction:
10x + 18 = -90
Subtract 18 from both sides:
10x = -108
Divide both sides by 10:
x = -108/10
Simplifying, we get:
x = -54/5
Therefore, the solution to the system of equations is (-54/5, 3/5).
This solution is not among the answer choices given.
Pick out of the answers I provided
None of the answers provided (-7.25, -1.25), (4, 1), (-6, -1), (5.25, 1.25) match the solution (-54/5, 3/5) that we found.
To solve the system of equations, we will use the method of substitution.
Step 1: Solve the second equation for y.
2 = 5y - 1
Add 1 to both sides:
2 + 1 = 5y - 1 + 1
3 = 5y
Divide both sides by 5:
3/5 = y
Step 2: Substitute the value of y into the first equation.
2x + 6y = -18
2x + 6(3/5) = -18
Multiply 6 and (3/5):
2x + 18/5 = -18
Subtract 18/5 from both sides:
2x = -18 - 18/5
To combine the fractions, convert -18 to a fraction with a denominator of 5:
2x = (-90/5) - (18/5)
2x = -108/5
Divide both sides by 2:
x = (-108/5) / 2
To divide fractions, multiply by the reciprocal of the divisor:
x = (-108/5) * (1/2)
Multiply the numerators and denominators:
x = -108/10
Reduce the fraction:
x = -54/5
Therefore, the solution to the system of equations is (-54/5, 3/5), which is approximately (-10.8, 0.6).
None of the given answer choices match the solution calculated.
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution to find the solution.
Step 1: Solve one equation for one variable.
Let's 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 other equation.
Now that we have the value of y, we can substitute it into the first equation:
2x + 6(3/5) = -18
2x + 18/5 = -18
Multiply both sides by 5 to eliminate the fraction:
10x + 18 = -90
Subtract 18 from both sides:
10x = -108
Divide both sides by 10 to solve for x:
x = -108/10
x = -10.8
So the solution to the system of equations is x = -10.8 and y = 3/5.
Now let's check the answer options:
A. (-7.25, -1.25): The x-value does not match the answer we found, so this option is incorrect.
B. (4, 1): The x-value does not match the answer we found, so this option is incorrect.
C. (-6, -1): The x-value does not match the answer we found, so this option is incorrect.
D. (5.25, 1.25): The x-value does not match the answer we found, so this option is incorrect.
Therefore, none of the provided answer options match the solution to the system of equations.