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#