Question

1) x/3 + y/4 = 4 x/2-y/4 = 1 2) x/12 + y/5 = 8 x/4 - y/7 = -2 Решите системы уравнений способом сложения

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the systems of equations using the method of addition (also known as the method of elimination), we need to eliminate one variable by adding the two equations together. This will create a new equation with only one variable, which we can then solve for that variable. Once we have the value of one variable, we can substitute it back into one of the original equations to find the value of the other variable.

Let's start with the first system of equations:

1. x/3 + y/4 = 4 x/2 - y/4 = 1

Step 1: Eliminate y by adding the two equations together.

(x/3 + y/4) + (x/2 - y/4) = 4 + 1

Step 2: Simplify the equation:

x/3 + x/2 = 5

Step 3: Get a common denominator (6 in this case):

(2x + 3x)/6 = 5

Step 4: Combine the x terms:

5x/6 = 5

Step 5: Solve for x:

5x = 5 * 6 5x = 30 x = 30/5 x = 6

Now that we have the value of x, let's find y by substituting the value of x into one of the original equations. Let's use the first equation:

x/3 + y/4 = 4 6/3 + y/4 = 4 2 + y/4 = 4 y/4 = 4 - 2 y/4 = 2

Now, solve for y:

y = 2 * 4 y = 8

So, the solution to the first system of equations is x = 6 and y = 8.

Now, let's move on to the second system of equations:

2. x/12 + y/5 = 8 x/4 - y/7 = -2

Step 1: Eliminate y by adding the two equations together.

(x/12 + y/5) + (x/4 - y/7) = 8 - 2

Step 2: Simplify the equation:

x/12 + x/4 = 6

Step 3: Get a common denominator (12 in this case):

(x + 3x)/12 = 6

Step 4: Combine the x terms:

4x/12 = 6

Step 5: Solve for x:

4x = 6 * 12 4x = 72 x = 72/4 x = 18

Now that we have the value of x, let's find y by substituting the value of x into one of the original equations. Let's use the first equation:

x/12 + y/5 = 8 18/12 + y/5 = 8 3/2 + y/5 = 8

Step 6: Subtract 3/2 from both sides:

y/5 = 8 - 3/2

Step 7: Find a common denominator (10 in this case):

y/5 = 16/2 - 3/2

Step 8: Combine the y terms:

y/5 = 13/2

Step 9: Solve for y:

y = (13/2) * 5 y = 65/2 y = 32.5

So, the solution to the second system of equations is x = 18 and y = 32.5.

To summarize:

1. x = 6 and y = 8
2. x = 18 and y = 32.5