Question

Consider the system of equations and the partial solution below.

6x+3y=9
5x+4y=10
Multiply the first equation by -4.
Multiply the second equation by 3.
Add the resulting system of equations.
Which terms will cancel when you add the resulting system of equations?
-36 and 36
-24x and 24x
O-15x and 15x
-12y and 12y

Answer 1

-15x and 15x is the answer

Answer 2

-12y and 12y

Explanation:

lets do the multiplication to each equation

`\left \{ {{(6x+3y)(-4)=9(-4)} \atop {(5x+4y)3=10(3)}} \right.`
this is

`\left \{ {{-24x-12y=-36} \atop {15x+12y=30}} \right.`
if we add the systems notice the values that do cancel are -12y and 12y
and the results of the adition is

`-9x=-6`
from this

`x=(-6)/(-9) =(2)/(3)`
and you can find y from any of the first equation.

`y=3-2x=3-(4)/(3) =\frac{5}3}`