Question

4x-y=7 2y+14=8x решите систему

Answer 1

4х-у=7
2у+14=8х

4х-у=7
2у-8х= -14

8х-2у=14
-8х+2у= -14

0=0

Если в целых числах, то система решения не имеет

Answer 2

To solve the system of equations, we'll use the method of substitution or elimination. Let's go with the substitution method.

Step 1: Solve one equation for one variable. Let's solve the first equation for y: 4x - y = 7 y = 4x - 7

Step 2: Substitute the expression for y into the second equation. 2y + 14 = 8x Replace y with (4x - 7): 2(4x - 7) + 14 = 8x

Step 3: Solve for x. Expand and simplify the equation: 8x - 14 + 14 = 8x 8x = 8x

Step 4: Determine the value of y. Now that we have 8x = 8x, it means that the equation is satisfied for any value of x. There are infinitely many solutions to this system of equations, which means any value of x can be chosen, and the corresponding value of y will be determined by the first equation.

Step 5: Write the solution. The system of equations has infinitely many solutions. One possible way to express the solution is: x = any real number (e.g., x = 0, x = 1, x = -5, etc.) y = 4x - 7 (corresponding y-value for each chosen x)

For example:

• If x = 0, then y = 4(0) - 7 = -7. So one solution is (x = 0, y = -7).
• If x = 1, then y = 4(1) - 7 = -3. So another solution is (x = 1, y = -3).
• If x = -5, then y = 4(-5) - 7 = -27. So yet another solution is (x = -5, y = -27).

Remember, there are infinitely many combinations of x and y that satisfy the system of equations.