Answer:
x = [tex]\frac{22}{7}[/tex]
y = [tex]\frac{3}7}[/tex]
Step-by-step explanation:
[tex]2x-3y=5\\5x=4y=14\\\\\left[\begin{array}{cc}2&-3\\5&-4\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right] =\left[\begin{array}{c}5\\14\\\end{array}\right][/tex]
Let A = [tex]\\\left[\begin{array}{cc}2&-3\\5&-4\\\end{array}\right][/tex]
The inverse of A multiplied by A = the identity matrix [tex]\left[\begin{array}{cc}1&0\\0&1\\\end{array}\right][/tex]
Inverse of A = [tex]\frac{1}{detA}[/tex] [tex]\left[\begin{array}{ccc}-4&3\\-5&2\\\end{array}\right][/tex]
detA = ad - bc = [tex]-8 - - 15 = 7[/tex]
Inverse of A = [tex]\left[\begin{array}{cc}\frac{-4}{7} &\frac{3}{7} \\\frac{-5}{7} &\frac{2}{7}\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{cc}\frac{-4}{7} &\frac{3}{7} \\\frac{-5}{7} &\frac{2}{7}\\\end{array}\right] \left[\begin{array}{ccc}5\\14\\\end{array}\right] = \left[\begin{array}{ccc}\frac{22}{7} \\\frac{3}{7} \\\end{array}\right][/tex]
