Answer:
x = 1 and y = 1.
Step-by-step explanation:
Given equations are :[tex]5x - 4y = 1 ...... (1) and\\2x + 3y = 5 .......(2)[/tex]
Now using equation (1)
[tex]5x - 4y = 1[/tex]
[tex]5x = 4y + 1[/tex]
[tex]x = \frac{4y + 1}{5}[/tex]
By substituting the value of x in equation 2
[tex]2x + 3y = 5[/tex]
[tex]2(\frac{4y + 1}{5}) + 3y = 5[/tex]
Further solving
[tex]\frac{8y+ 2}{5} + 3y = 5[/tex]
[tex]8y + 2 + 15y = 25[/tex]
[tex]23y = 25 - 2 = 23[/tex]
[tex]y = 23/23 = 1[/tex]
Now substituting the value of y in x,
[tex]x = \frac{4y + 1}{5}[/tex]
[tex]x = \frac{4 (1) + 1}{5} = \frac{5}{5} = 1[/tex]
