Question

How do you solve the system of equations `2x + 5y = 15` and `5x + 10y = 35`?

Answer 1

`x = 5 and y =1`

Explanation:

Before jumping in and choosing your favourite method, look at the options available first.

ELimination seems obvious, because 5y can be multiplied by -2 to give -10y,

Notice that the second equation can be divided by 5, which will make all the numbers smaller.

`5x + 10y = 35 " becomes " x + 2y = 7`
This can be written as `x = 7-2y" "` so substitution is a viable method as well.

Now that we have looked, we can make a better decision about the best method.
Elimination:

`" " 2x + 5y = 15 ....................."A"`
`" " 5x + 10y = 35 ..................."B"`

`" A x -2: " -4x -10 y = -30`
`" A + C: gives " x = 5`

Subst in A: `" "2xx5 + 5y = 15 rArr 5y = 5`

`" "y = 1`

OR Substitution: `" "2x + 5y = 15 " and "x = 7-2y`

Substitute for x:

`2(7-2y) + 5y = 15`
`14 -4y + 5y = 15`
`" " y = 1 " then " x = 7-2(1)`
`" "x=5`