Answer:
[tex]\large \boxed{x= 18; y = 5}[/tex]
Step-by-step explanation:
1. Calculate x
[tex]\begin{array}{rcll}7x - 23 & = & 3x + 49 & \text{Corresponding angles}\\7x & = & 3x + 72 & \text{Added 23 to each side}\\4x & = & 72 & \text{Subtracted 3x from each side}\\x & = & \mathbf{18} & \text{Divided each side by 4}\\\end{array}[/tex]
2. Calculate y
[tex]\begin{array}{rcll}3x & = & 11y - 1 & \text{Corresponding angles}\\3 \times 18 & = & 11y - 1 & \text{Substituted the value of x}\\54 & = & 11y - 1 &\text{Simplified}\\55 & = & 11y & \text{Added 1 to each side}\\y & = & \mathbf{5} & \text{Divided each side by 11}\\\end{array}\\\large \boxed{\mathbf{x= 18; y = 5}}[/tex]
Check:
7×18 - 23 = 3 × 18 + 49 3 × 18 = 11 × 5 - 1
126 - 23 = 54 + 49 54 = 55 - 1
103 = 103 54 = 54
OK.
