Question

Solve the simultaneous equations

4x + 5y = 4
2x - y = 9
Show clear algebraic working.

Answer 1

`x= \frac 72, ~~y= -2`

Step by step explanation:

`4x+5y=4~~~...(i)\\\\2x-y=9~~~...(ii)\\\\\text{Multiply eq (ii) by 2 to isolate x:}\\\\4x-2y=18~~~.....(iii)\\\\(iii)-(i):\\\\4x-2y-4x-5y=18-4\\\\\implies -7y=14\\\\\implies y = -\frac{14}7 = -2\\\\\text{Substitute}~ y=-2~ \text{in equation (iii):}\\\\4x-2(-2) = 18\\\\\implies 4x +4 = 18\\\\\implies 4x = 18-4\\\\\implies 4x = 14\\\\\implies x = \frac{14}4 = \frac 72\\\\\text{Hence}~ (x,y) =\left(\frac 72 , -2 \right)`

Answer 2

Explanation:

4x+5y=4 (equation 1)

2x-y=9 (equation2)

solving equation 1 and 2 and multiplying equation 2 by 2

4x+5y=4

4x-2y=18

- + -

________

7y= -14

y= -2

putting the value of y in equation 2

2x-y=9

2x+2=9

2x=7

x=3.5