8. ) 4x-7y=7 12x-21y=24

To solve the system of linear equations:<br /><br />\[<br />\left\{<br />\begin{array}{l}<br />4x - 7y = 7 \\<br />12x - 21y = 24<br />\end{array}<br />\right.<br />\]<br /><br />we can use the method of elimination or substitution. Let's start by examining the second equation.<br /><br />First, notice that the second equation is a multiple of the first equation:<br />\[ 12x - 21y = 3(4x - 7y) \]<br /><br />So, let's multiply the first equation by 3 to see if it matches the second equation:<br />\[ 3(4x - 7y) = 3 \cdot 7 \]<br />\[ 12x - 21y = 21 \]<br /><br />Now we have:<br />\[ 12x - 21y = 21 \]<br />and<br />\[ 12x - 21y = 24 \]<br /><br />These two equations are contradictory because \(21 \neq 24\). Therefore, there is no solution to this system of equations. The system is inconsistent.