Question

Solve the simultaneous equation 4x+7y=1 3x+10y=15

Answer 1

4x + 7y = 1
3x + 10y = 15

Multiply the first equation by -3, and the 2nd by 4.

-12x - 21y = -3
12x + 40y = 60

Add the equations:

19y = 57

y = 3

Plug this into any of the two equations to find 'x':

4x + 7y = 1

4x + 7(3) = 1

4x + 21 = 1

Subtract 21 to both sides:

4x = -20

Divide 4 to both sides:

x = -5

So our solution is (-5, 3)

Answer 2

4x +   7y = 1   ⇒ 12x + 21y = 3
3x + 10y = 15 ⇒ 12x + 40y = 60
                                    -19y = -57
                                     -19     -19
                                         y = 3
                             4x + 7(3) = 1
                               4x + 21 = 1
                                     - 21  - 21
                                       4x = -20
                                        4       4 
                                         x = -5
                                   (x, y) = (-5, 3)