Question

Please solve the combination of equations here.

Answer 1

`\left \{ {{x=5} \atop {y=7}} \right.`

Explanation:

`\left \{ {{x+y=12} \atop {3y = 4x+1}} \right.`

`\left \{ {{x=12-y} \atop {3y=4x+1}} \right.`

We are going to do a replacement of x for a second equation

So instead

`3y=4x+1`

in the place of x we are putting 12-y from the first equation, so

`3y = 4(12-y)+1`

To leave the brackets we need to do multiplication

`3y = 4*12-4*y+1`

Which is

`3y = 48-4y+1`

`3y = -4y+49 /+4y\\7y = 49 /:7\\y = 7`

How to determine x? From the first equation:

If the x +y = 12 then the x = 12-y so x = 12-7 = 5

We should write solution as a pair:

`\left \{ {{x=5} \atop {y=7}} \right.`