Solve by the elimination method.
6x−5y=
47
5x+7y=
−39
.
.
.
Question content area right
Part 1
What is the solution set of the system? Select the correct choice below and, if necessary, fill in the answer box to complete your answer.
A.
The solution is enter your response here .
(Simplify your answer. Type an ordered pair.)
B.
There are infinitely many solutions. The solution set is x,enter your response here.
(Simplify your answer. Type an expression in terms of x.)
C.
The solution is the empty set.
To solve by the elimination method, we need to eliminate one variable by adding the equations together or subtracting one equation from the other. Let's multiply the first equation by 5 and the second equation by 6 to make the coefficients of y the same:
30x - 25y = 235
30x + 42y = -234
Now, we can subtract these two equations to eliminate the x variable:
(30x - 25y) - (30x + 42y) = 235 - (-234)
-67y = 469
y = -7
Substituting this value of y into one of the original equations, we can solve for x:
6x - 5(-7) = 47
6x + 35 = 47
6x = 12
x = 2
Therefore, the solution to the system of equations is (x, y) = (2, -7).
The correct choice is A. The solution is (2, -7).
To solve the system of equations by the elimination method:
Step 1: Multiply both sides of the first equation by 7 and the second equation by 5 to obtain the same coefficient for the y variable.
7(6x - 5y) = 7(47)
5(5x + 7y) = 5(-39)
Simplifying, we get:
42x - 35y = 329
25x + 35y = -195
Step 2: Add the two equations together to eliminate the y variable.
(42x - 35y) + (25x + 35y) = 329 + (-195)
Simplifying, we get:
67x = 134
Step 3: Divide both sides of the equation by 67 to solve for x.
67x/67 = 134/67
x = 2
Step 4: Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation.
6x - 5y = 47
6(2) - 5y = 47
12 - 5y = 47
-5y = 47 - 12
-5y = 35
y = 35/-5
y = -7
So the solution to the system of equations is (2, -7).
Therefore, the correct answer is A. The solution is (2, -7).
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations.
Given the two equations:
6x - 5y = 47 ........(Equation 1)
5x + 7y = -39 ........(Equation 2)
To eliminate the variable y, we can multiply Equation 1 by 7 and Equation 2 by 5 to make the coefficients of y the same:
(7)(6x - 5y) = (7)(47)
(5)(5x + 7y) = (5)(-39)
Simplifying, we get:
42x - 35y = 329 ........(Equation 3)
25x + 35y = -195 ........(Equation 4)
Now, add Equation 3 and Equation 4 together to eliminate the y variable:
(42x - 35y) + (25x + 35y) = 329 + (-195)
Simplifying, we get:
67x = 134
Divide both sides by 67 to solve for x:
x = 134 / 67
x = 2
Now substitute this value of x back into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:
6(2) - 5y = 47
12 - 5y = 47
-5y = 47 - 12
-5y = 35
Divide both sides by -5 to solve for y:
y = 35 / -5
y = -7
The solution to the system of equations is (x, y) = (2, -7).
Therefore, the correct choice is A. The solution is (2, -7).