Solve the system of equations.
2x+6y=−18
x=5y−1 (1 point)
Responses
(−7.25, −1.25)
left parenthesis negative 7.25 comma negative 1.25 right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(−6, −1)
left parenthesis negative 6 comma negative 1 right parenthesis
(5.25, 1.25)
To solve the system of equations, we can substitute the value of x from the second equation into the first equation:
2x + 6y = -18
2(5y-1) + 6y = -18
10y -2 + 6y = -18
16y -2 = -18
16y = -16
y = -1
Now that we have the value of y, we can substitute it back into the second equation to solve for x:
x = 5y - 1
x = 5(-1) - 1
x = -5 - 1
x = -6
Therefore, the solution to the system of equations is (x, y) = (-6, -1).
To solve the system of equations, we will substitute the value of x from the second equation into the first equation.
Given equation 1: 2x + 6y = -18
Given equation 2: x = 5y - 1
Substituting x = 5y - 1 into equation 1:
2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -16/16
y = -1
Now that we have the value of y, we can substitute it back into either of the original equations to find the value of x.
Using equation 2: x = 5y - 1
x = 5(-1) - 1
x = -5 - 1
x = -6
Therefore, the solution to the system of equations is x = -6 and y = -1. So the answer is (−6, −1).
To solve the system of equations:
1. Substitute the value of x from the second equation into the first equation.
2. Simplify the resulting equation to solve for y.
3. Substitute the value of y back into either of the original equations to find the value of x.
Let's go through the steps:
Given equations:
1) 2x + 6y = -18
2) x = 5y - 1
Step 1: Substitute x in equation 1 with the expression 5y - 1 from equation 2:
2(5y - 1) + 6y = -18
Simplifying equation 1:
10y - 2 + 6y = -18
16y - 2 = -18
Step 2: Solve for y by isolating it:
16y = -18 + 2
16y = -16
y = -16/16
y = -1
Step 3: Substitute the value of y (-1) into equation 2 to find x:
x = 5(-1) - 1
x = -5 - 1
x = -6
The solution to the system of equations is x = -6 and y = -1.
Therefore, the correct answer is (-6, -1).