Question

How do you solve the system of equations `4h + 3b = 27` and `7h + 4b = 41`?

Answer 1

`(h,b)=(3,5)`

Explanation:

We have:

`4h+3b=27`
`7h+4b=41`

I'm not seeing any straightforward operations we can do, so I'll move on to adjusting both equations. I'm going to multiply through in both equations to generate a `b` term that I can then add one to the other:

`4(4h+3b)=4(27)`
`-3(7h+4b)=-3(41)`

`color(white)(-00)16h+12b=color(white)(-0)108`
`ul(color(white)(0)-21h-12b=-123)`
`color(white)(00)-5hcolor(white)(000000)=-15=>color(blue)(ul(bar(abs(color(black)(h=3))))`

We can now substitute back into an original equation to solve for `b`:

`4h+3b=27`

`4(3)+3b=27`

`12+3b=27`

`3b=15`

`color(blue)(ul(bar(abs(color(black)(b=5))))`