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  • If 2x + y = 23 and 4x – y = 19, find the values of 5y – 2x and y by x -2

If 2x + y = 23 and 4x – y = 19, find the values of 5y – 2x and \frac{y}{x}-2

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Solution:
Given equations are
2x + y = 23 … (1)
4x – y = 19 … (2)
Using elimination method in equation (1) and (2) we get
2x + y = 23
4x – y = 19
6x = 42
x = \frac{42}{6}= 7
Put x = 7 in equation (1) we get
2(7) + y = 23
y = 23 – 14
y = 9
Now 5y – 2x = 5(9) – 2 (7)
= 45 – 14
= 31

\frac{y}{x}- 2= \frac{9}{7}-2

\frac{y-14}{7}= \frac{-5}{7}

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