Answer:
x = 4 and y = 5
Explanation:
To solve this system of equations by elimination, we want to eliminate one of the variables so that we end up with an equation involving only the other variable. We can do this by multiplying one or both of the equations by a constant so that when we add the two equations together, one of the variables will cancel out.
We notice that if we multiply the second equation by 2, we can eliminate the y variable by adding the two equations together:
-6x + 5y = 1 (first equation)
-3x + 2y = -2 (second equation, multiplied by 2)
-6x + 5y = 1
-6x + 4y = -4 (adding the two equations)
Now, we can eliminate the x variable by subtracting the second equation from the first:
-6x + 5y = 1
-(-6x + 4y = -4) (note the double negative here)
Simplifying, we get:
-6x + 5y = 1
6x - 4y = 4
Adding the two equations together, we can eliminate the x variable again:
-6x + 5y = 1
+6x - 4y = 4
y = 5
Now that we know y = 5, we can substitute this value back into one of the original equations to solve for x:
-6x + 5y = 1
-6x + 5(5) = 1
-6x + 25 = 1
-6x = -24
x = 4
Therefore, the solution to the system of equations -6x+5y=1 and -3x+2y=-2 is x = 4 and y = 5.