Question

7x + 2 y = - 13 4x - 5y = - 32 решить систему способом сложения

Answer 1

Это очень простой пример, разберись удачи

Answer 2

To solve the system of equations using the method of addition (also known as the method of elimination or the method of linear combination), we'll manipulate the equations in such a way that when we add them, one of the variables will be eliminated. Here are the steps to solve the system:

Step 1: Ensure the coefficients of one of the variables in both equations are the same (or additive inverses) when added. Step 2: Add the modified equations to eliminate one variable. Step 3: Solve for the remaining variable. Step 4: Substitute the found value back into one of the original equations to find the other variable.

Let's proceed with the given system of equations:

1. 7x + 2y = -13
2. 4x - 5y = -32

Step 1: We need to manipulate the equations to make the coefficients of one of the variables the same when added. Let's make the coefficients of y the same:

Multiply the first equation by 5 and the second equation by 2, so the coefficients of y become -10 and -10, respectively:

5 * (7x + 2y) = 5 * (-13) 2 * (4x - 5y) = 2 * (-32)

This gives us the modified equations:

3. 35x + 10y = -65
4. 8x - 10y = -64

Step 2: Now, add the modified equations (equation 3 + equation 4):

(35x + 10y) + (8x - 10y) = -65 - 64

Step 3: The y term cancels out, leaving us with:

43x = -129

Step 4: Now, solve for x:

x = -129 / 43 x = -3

Step 5: Substitute the value of x into either of the original equations to find y. Let's use equation 1:

7x + 2y = -13 7(-3) + 2y = -13 -21 + 2y = -13 2y = -13 + 21 2y = 8 y = 8 / 2 y = 4

So, the solution to the system of equations is x = -3 and y = 4.