The solutions are:
[tex]x = 18\\y = 5[/tex]
[tex]49^{\circ} +(3x)^{\circ} = (7x - 23)^{\circ}\\[/tex] (corresponding angles are congruent)
Solve for x
[tex]49+3x = 7x - 23\\[/tex]
Add like terms
[tex]49+3x = 7x - 23\\49 +23 = 7x -3x\\72 = 4x\\[/tex]
Divide both sides by 4
[tex]18 = x\\x = 18[/tex]
Find the value of y:
[tex]3x = 11y - 1[/tex] (correspindning angles)
Plug in the value of x
[tex]3x = 11y - 1\\3(18) = 11y - 1\\54 = 11y - 1[/tex]
Add 1 to both sides
[tex]54 + 1 = 11y\\55 = 11y[/tex]
Divide both sides by 11
[tex]5 = y\\y = 5[/tex]
Thus:
[tex]x = 18\\y = 5[/tex]
Learn more about corresponding angles here:
https://brainly.com/question/21712003
