Answer:
x = 6; y = 20
Step-by-step explanation:
Given two numbers one large and one small.
[tex]$ x $[/tex] is the smaller number and [tex]y[/tex] is the larger number.
According to the first statement we have:
[tex]$ 3y = 5x + 30$[/tex]
Rearranging we get:
[tex]$ 5x - 3y = - 30 \hspace{15mm} (1) $[/tex]
From the second statement, we have:
[tex]$ 5x + y = 50 \hspace{15mm} (2) $[/tex]
These two lines are plotted on the graph. The point at which the two lines intersect will give the two numbers.
To solve (1) and (2) we subtract the two equations:
[tex]$ - 4y = - 80 $[/tex]
[tex]$ \implies y = 20 $[/tex]
Substituting the value of [tex]y[/tex], in the equation we get:
[tex]$ 5x = 50 - 20 = 30 $[/tex]
[tex]$ \implies x = 6 $[/tex].
Therefore, the values are: (x, y) = (6, 20).
