Simultaneous Equation 4x-4y=24\\x-4y=3 Im looking for more of an explanation than an answer. Thanks

Question

Simultaneous Equation


`4x-4y=24\\x-4y=3`

Im looking for more of an explanation than an answer. Thanks

Answer 1

You have to either get rid of y or x to find the result of the intercepts. In this case because you have to substract both equations it’s better if we get rid of y which is easier as both the signs are negative(-4 and -4) so -4- -4 is -4+4 which is o
4x-x=3x and 24-3=21
So our equation now is 3x=21 to find x you have to rearrange dividing 21/3=7
Hence, x=7 substitute it in one of the two equations given. In this case I’m going to substitute it in the second one which easiest.
(7)-4y=3. -4y=3-7. -4y=-4. So y=-4/-4 =1
Therefore (7,1) x=7. y=1

Answer 2

You're looking for values of x and y that satisfy both equations at the same time. We can solve this by substitution, which involves solving one equation for one of the variables, then rewriting the other equation completely in terms of one of these variables, and solving for them.

In the second equation, we have

x - 4y = 3

which means

x = 4y + 3

Substitute this into the other equation and solve for the other variable:

4x - 4y = 24

4 (4y + 3) - 4y = 24

16y + 12 - 4y = 24

12y + 12 = 24

12y = 12

y = 1

Solve for the remaining variable:

x = 4y + 3

x = 4•1 + 3

x = 4 + 3

x = 7