Question

6x-12y=-6 -56x+2y=-54 решить функцыю методом додавання

Answer 1

надеюсь, ты поймешь мой почерк

Answer 2

To solve the system of equations using the method of addition (also known as the method of elimination or the method of adding equations), we'll add the two equations together to eliminate one variable and then solve for the other variable. Here are the steps:

Step 1: Multiply the two equations to make the coefficients of either x or y in both equations equal:

Multiply the first equation by 2 and the second equation by -1 to make the coefficients of y the same:

Equation 1: 2(6x - 12y) = 2(-6) --> 12x - 24y = -12 Equation 2: -1(-56x + 2y) = -1(-54) --> 56x - 2y = 54

Step 2: Add the modified equations together to eliminate y:

(12x - 24y) + (56x - 2y) = -12 + 54

Step 3: Simplify the equation:

12x + 56x - 24y - 2y = 42x - 26y = 42

Step 4: Solve for x:

42x = 42 x = 42 / 42 x = 1

Step 5: Substitute the value of x into one of the original equations to find y. We'll use the first equation:

6x - 12y = -6 6(1) - 12y = -6 6 - 12y = -6

Step 6: Solve for y:

-12y = -6 - 6 -12y = -12 y = -12 / -12 y = 1

Step 7: Check the solution by substituting the values of x and y into the second equation:

-56x + 2y = -54 -56(1) + 2(1) = -54 -56 + 2 = -54 -54 = -54

Since both equations hold true when x = 1 and y = 1, the solution is correct. The solution to the system of equations is x = 1 and y = 1.