Question

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

Answer 1

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`