Answer :
[tex]\begin{cases} 6x + 5y = 10 \\ 7x - 3y = 24 \end{cases}\\\begin{cases} 5y = -6x+10\ \ / :5 \\ 7x - 3y = 24 \end{cases}\\\begin{cases} y =-\frac{6}{5}x+2 \\ 7x - 3y = 24 \end{cases}\\\\substition \\[/tex]
[tex]7x - 3y = 24 \\ 7x - 3 \cdot (-\frac{6}{5}x+2) = 24\\7x+\frac{18}{5}x-6=24\\ \frac{35}{5}x+\frac{18}{5}x =24 +6\\\frac{53}{5}x =30 \ \ / \cdot \frac{5}{53}\\\\x=\frac{150}{53}[/tex]
[tex]y= -\frac{6}{5}x+2 \\y= -\frac{6}{5} \cdot \frac{150}{53} +2\\y=-\frac{6\cdot 30}{53}+2\\y=-\frac{180}{53}+ \frac{106}{53}\\ \\ y= -\frac{74}{53}\\\\ Answer : x=\frac{150}{53} \ \ and \ \y= -\frac{74}{53}[/tex]
[tex]7x - 3y = 24 \\ 7x - 3 \cdot (-\frac{6}{5}x+2) = 24\\7x+\frac{18}{5}x-6=24\\ \frac{35}{5}x+\frac{18}{5}x =24 +6\\\frac{53}{5}x =30 \ \ / \cdot \frac{5}{53}\\\\x=\frac{150}{53}[/tex]
[tex]y= -\frac{6}{5}x+2 \\y= -\frac{6}{5} \cdot \frac{150}{53} +2\\y=-\frac{6\cdot 30}{53}+2\\y=-\frac{180}{53}+ \frac{106}{53}\\ \\ y= -\frac{74}{53}\\\\ Answer : x=\frac{150}{53} \ \ and \ \y= -\frac{74}{53}[/tex]
