Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-3x – 5y = 61
7x – 5y = -9
Subtract the second equation from the first.
-10x = 70
x = 70/-10 = -7
To solve this system of equations using the elimination method, we will eliminate one variable by adding or subtracting the equations.
First, let's multiply the second equation by 3 to make the coefficients of x in both equations equal:
3 * (7x - 5y) = 3 * (-9)
21x - 15y = -27
Now we have our system of equations:
-3x - 5y = 61
21x - 15y = -27
We can eliminate the y variable by adding the two equations:
(-3x - 5y) + (21x - 15y) = 61 + (-27)
-3x + 21x - 5y - 15y = 34
Combine like terms:
18x - 20y = 34
Now we have one equation with one variable. Let's proceed solving for x:
18x = 34 + 20y
x = (34 + 20y) / 18
We could solve for y by substituting this value of x into either of the original equations, but it's not necessary for the given question.
Therefore, the solution to the system of equations is x = (34 + 20y)/18. There is no unique solution because the equation contains the variable y, indicating an infinite number of solutions.