Question

I am having a hard time with simultaneous equations specifically the elimination method, i want to know when do we subtract and when do we add, so if u know how its done plz help im confused

Example :
3x-2y =7
4x+y = 13

Plz solve it too-

Answer 1

The solution to these two equations is (3, 1)

Explanation:

So for the elimination method, we are basically multiply each equation by a factor that would allow us to cancel them out..

We could rewrite the equations as the following to make the elimination method easier:

-2y + 3x = 7

y + 4x = 13

We could multiply the second equation by positive 2 in order to cancel out the y from the first equation when we add.

-2y + 3x = 7

2y + 8x = 26 ---> Now we have 11x = 33, when we simplify, we have x = 3.

Now to find our y value in order to find the solution, we would just plug in our x value and solve for y. **We can use either equation to find the answer for this...

-2y + 3x =7.

-2y + 3(3) = 7

-2y + 9 = 7

-2y = -2

y = 1.

We can double check our answer by plugging in both x and y values into the second equation.

4(3) + 1 = 13.

12 + 1 = 13, so we are correct.

The solution to these two equations is (3, 1)