Tính cấp số cộng sau biết; u7-4u5+u3=-18; u1+2u2+3u3-u4=15

To solve this system of equations, we can use the method of elimination or substitution. Let's use the method of elimination.

First, let's rearrange the equations to have the variables in the same order:

1) u7 - 4u5 + u3 = -18
2) u1 + 2u2 + 3u3 - u4 = 15

To eliminate the u3 term, we can multiply equation 1 by 3 and equation 2 by -1:

3) 3(u7 - 4u5 + u3) = 3(-18)
4) -1(u1 + 2u2 + 3u3 - u4) = -1(15)

Simplifying these equations, we get:

5) 3u7 - 12u5 + 3u3 = -54
6) -u1 - 2u2 - 3u3 + u4 = -15

Now, let's add equations 5 and 6 together:

7) 3u7 - 12u5 + 3u3 - u1 - 2u2 - 3u3 + u4 = -54 - 15

Simplifying this equation, we get:

8) 3u7 - 12u5 - u1 - 2u2 + u4 = -69

So, the simplified system of equations is:

9) 3u7 - 12u5 - u1 - 2u2 + u4 = -69
10) u1 + 2u2 + 3u3 - u4 = 15

Now, we can solve this system of equations using any method of our choice.