Solving Equations Using Substitution Quick Check
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Question
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
(5.25, 1.25)
left parenthesis 5.25 comma 1.25 right parenthesis
(−6, −1)
To solve the system of equations, we will substitute the value of x from the second equation into the first equation.
Substitute x=5y-1 into the first equation:
2(5y-1)+6y=-18
10y-2+6y=-18
16y-2=-18
16y=-16
y = -1
Now substitute y=-1 into the second equation to find x:
x=5(-1)-1
x = -6
Therefore, the solution to the system of equations is (-6, -1).
To solve the system of equations using substitution, follow these steps:
Step 1: Solve one equation for one variable.
Given the equations:
2x + 6y = -18 ...(Equation 1)
x = 5y - 1 ...(Equation 2)
Let's solve Equation 2 for x:
x = 5y - 1
Step 2: Substitute the expression found in Step 1 into the other equation.
Substitute x = 5y - 1 into Equation 1:
2(5y - 1) + 6y = -18
Step 3: Simplify and solve for y.
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1
Step 4: Substitute the value of y back into Equation 2 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 (-6, -1).
To solve the system of equations using substitution, we can substitute the expression for x from the second equation into the first equation and solve for y.
Given equations:
1) 2x + 6y = -18
2) x = 5y - 1
Substitute the expression for x from the second equation into the first equation:
2(5y - 1) + 6y = -18
Simplify the equation:
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1
Now substitute the value of y back into the second equation to find the value of x:
x = 5(-1) - 1
x = -5 - 1
x = -6
So the solution to the system of equations is (x, y) = (-6, -1).
Therefore, the correct answer is option (−6, −1).