Chapter 13, Trigonometric Ratios and Functions - 13.1 Use Trigonometry with Right Triangles - 13.1 Exercises - Mixed Review - Page 858: 44

$x=5; y=2$

Since we are given two equations $2x-y= 8$ and $3x+4y=23$ Now, multiply the equation $2x-y= 8$ by $4$. we have $8x-4y= 32$ and $3x+4y=23$ After solving, we get $11x=55 \implies x=5$ Then, $3(5)+4y=23$ This implies $ 15+4y=23 \implies y=2$ Hence, $x=5; y=2$