### solution to homogeneous system of linear equations with coefficients over field $\mathbb{F}_2$

Solve the following homogeneous systems of linear equations with coefficients over field $\mathbb{F}_2$:

```
x1+x2+x3+x4+x5+x6+x7 = 0
x1=0
x2+x3+x4 =0
x5=0
```

I want to output on the sage following:

```
x1=x5=0
x6=x7
x2+x3+x4=0
```

I want to solve a general homogeneous systems with coefficients over field $\mathbb{F}_2$ and output same as above.

I hope that someone can help. Thanks!