Question

Решите систему уравнений x+y=6, 3x-8y=7 способом сложения

Answer 1

Умножим первое уравнение на 8
8х+8у=48
сложим его со вторым
11х=55
поделим на 11
х=5
вернемся к первому
у+5=6
у=1
Ответ: х=5
у=1

Answer 2

Solving the System of Equations using the Method of Addition

To solve the system of equations \(x + y = 6\) and \(3x - 8y = 7\) using the method of addition, we can manipulate the equations to eliminate one of the variables when adding them together.

First, let's manipulate the equations to prepare them for addition.

We can multiply the first equation by 8 to make the coefficients of \(y\) in both equations equal:

Equation 1: \(8(x + y) = 8 \times 6\) Equation 2: \(3x - 8y = 7\)

This gives us:

Equation 1: \(8x + 8y = 48\) Equation 2: \(3x - 8y = 7\)

Now, we can add the two equations together to eliminate the variable \(y\):

\(8x + 8y + 3x - 8y = 48 + 7\) \(11x = 55\)

Now, we can solve for \(x\):

\(x = \frac{55}{11}\) \(x = 5\)

Next, we can substitute the value of \(x\) back into one of the original equations to solve for \(y\:

Using the first equation \(x + y = 6\):

\(5 + y = 6\) \(y = 1\)

So, the solution to the system of equations is: \(x = 5\) \(y = 1\)