Question

How do you solve the system `13x + 5y = 16` and `x = 4y + 10`?

Answer 1

`color(purple)({x,y=2,-2}`

Explanation:

`"Solve by substitution"`

`color(blue)(13x+5y=16` `(1st` `"equation")`

`color(blue)(x=4y+10` `(2nd` `"equation")`

`"As we can see,"` `x=4y+10,`

`"we can substitute it to the first equation"`

`rarr13(4y+10)+5y=16`

`"Use the distributive property -"` `color(brown)(a(b+c)=ab+ac`

`rarr(52y+130)+5y=16`

`rarr52y+130+5y=16`

`rarr57y+130=16`

`rarr57y=16-130`

`rarr57y=-114`

`rarrcolor(green)(y=-144/57=-2`

`"Now,substitute the value of y to the second equation"`

`rarrx=4(-2)+10`

`rarrx=-8+10`

`rarrcolor(green)(x=2`

`color(purple)({x,y=2,-2}`