Question

Решите систему у+z=9.5 x+y=8 x+z=8.5

Answer 1

You can solve like this

Answer 2

To solve the system of equations, we'll use the method of substitution or elimination. Let's start by using the method of elimination:

Given the system of equations:

1. u + z = 9.5 ...(i)
2. x + y = 8 ...(ii)
3. x + z = 8.5 ...(iii)

Step 1: Subtract equation (iii) from equation (2) to eliminate 'x'. Equation (ii) - Equation (iii): (x + y) - (x + z) = 8 - 8.5 y - z = -0.5 ...(iv)

Step 2: Add equation (i) and equation (iii) to eliminate 'z'. Equation (i) + Equation (iii): (u + z) + (x + z) = 9.5 + 8.5 u + x + 2z = 18 ...(v)

Step 3: Now we have two equations with 'y - z' and 'u + x + 2z'. We can solve these two equations simultaneously.

Step 4: Solve equations (iv) and (v):

(iv) y - z = -0.5 (v) u + x + 2z = 18

Since we don't have a direct equation for 'x' or 'y', we cannot directly find their values. However, we can express 'x' and 'y' in terms of other variables:

From equation (ii): x + y = 8 x = 8 - y ...(vi)

From equation (iii): x + z = 8.5 x = 8.5 - z ...(vii)

Now, we can express 'x' in terms of 'y' and 'z' in two different ways (equations vi and vii). Equating these expressions:

8 - y = 8.5 - z

Solving for 'z': z = y - 0.5 ...(viii)

Now, we can substitute equation (viii) into equation (iv) to solve for 'y - z':

y - (y - 0.5) = -0.5 y - y + 0.5 = -0.5 0.5 = -0.5

The above equation is not true, which means there is no solution for this system of equations. The given equations are inconsistent and cannot be satisfied simultaneously. This could be due to an error in the original equations or a mistake during the transcription of the problem. Double-check the equations to ensure their accuracy.