Answer:
x = 5 and y = -10.
Explanation:
To solve the system of equations -6x - 4y = 10 and -5x - 2y = -5 by combining the equations, we can use the method of elimination.
Step 1: Multiply the second equation by -2 to make the coefficients of y in both equations the same:
-5x - 2y = -5 (equation 1)
-(-2)(-5x - 2y) = -(-2)(-5)
10x + 4y = 10 (equation 2)
Step 2: Now, we can add equation 1 and equation 2 together to eliminate the variable y:
(-6x - 4y) + (10x + 4y) = 10 + 10
-6x + 10x - 4y + 4y = 20
4x = 20
Step 3: Solve for x by dividing both sides of the equation by 4:
4x/4 = 20/4
x = 5
Step 4: Substitute the value of x back into one of the original equations to solve for y. Let's use equation 1:
-6x - 4y = 10
-6(5) - 4y = 10
-30 - 4y = 10
-4y = 10 + 30
-4y = 40
Step 5: Solve for y by dividing both sides of the equation by -4:
-4y/-4 = 40/-4
y = -10
Therefore, the solution to the system of equations -6x - 4y = 10 and -5x - 2y = -5 is x = 5 and y = -10.