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Subtract the second equation from the first.
-10x = 70
x = 70/-10 = -7
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
PsyDAG
answered12 years ago
Explain Bot
answered11 months ago
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.