What are the values of b and c for which the equations x+5y=4 and 2x+by=c?

1 Answer
Jan 29, 2018

Please see the process steps below;

Explanation:

Method 1

Comparing..

We have;

x + 5y = 4

darr color(white)x darr color(white)(xx) darr

2x + by = c

Simply without solving if we compare we should have;

x + 5y = 4 rArr 2x + by = c

Hence;

x rArr 2x

+color(blue)5y rArr +color(blue)by

Therefore, b = 5

4 rArr c

Therefore, c = 4

Method 2

Solving simultaneously..

Using Elimination Method!

x + 5y = 4 - - - - - - eqn1

2x + by = c - - - - - - eqn2

Multiplying eqn1 by 2 and eqn2 by 1

2 (x + 5y = 4)

1 (2x + by = c)

2x + 10y = 8 - - - - - - eqn3

2x + by = c - - - - - - eqn4

Subtract eqn4 from eqn3

(2x - 2x) + (10y - by) = 8 - c

0 + 10y - by = 8 - c

10y - by = 8 - c

But, by = c - 2x

Hence;

10y - (c - 2x) = 8 - c

10y -c + 2x = 8 - c

10y + 2x = 8 -> "Equation"

Same thing as rArr 5y + x = 4

Proof:

Substitute eqn1 into the above equation..

10y + 2[4 - 5y] = 8

10y + 8 - 10y = 8

0 = 0

Hence;

b = 5 and c = 4