To solve the given system of equations, we need to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations simultaneously:
[tex]\[ 5x - 7y - 21 = 0 \][/tex]
[tex]\[ 25x - 35y = 63 \][/tex]
### Step-by-Step Solution:
#### 1. Simplify the equations if possible:
First, let's simplify the second equation. We notice that both the left-hand side and right-hand side can be divided by 5:
[tex]\[ 25x - 35y = 63 \][/tex]
[tex]\[ 5(5x - 7y) = 63 \][/tex]
[tex]\[ 5x - 7y = \frac{63}{5}\][/tex]
The second equation is now:
[tex]\[ 5x - 7y = 12.6 \][/tex]
So, our system of equations becomes:
[tex]\[ 5x - 7y - 21 = 0 \][/tex]
[tex]\[ 5x - 7y = 12.6 \][/tex]
#### 2. Rewrite the first equation to match the format of the second equation for elimination:
[tex]\[ 5x - 7y = 21 \][/tex]
Now, our system is:
[tex]\[ 5x - 7y = 21 \][/tex]
[tex]\[ 5x - 7y = 12.6 \][/tex]
#### 3. Subtract the second equation from the first:
Since both left sides and the right sides are equal, we subtract the second equation from the first:
[tex]\[ (5x - 7y) - (5x - 7y) = 21 - 12.6 \][/tex]
[tex]\[ 0 = 8.4 \][/tex]
We end up with [tex]\( 0 = 8.4 \)[/tex], which is a contradiction and indicates there are no values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that can simultaneously satisfy both equations.
### Conclusion:
Hence, the given system of equations has no solution. This means the system is inconsistent.
