Question 59409
Hi Stephanie,
There are many ways of solving two linear equations with two unknowns.
The simpler one is eliminating one variable and arriving at one equation with one variable.

Let me take an example and explain it to you.
Consider the two equations

2x+3y = 7------------(1)
x+7y = 9--------------(2)

For these two equations when we add or subtract them directly, we find that none of the variable gets cancelled.

So to eliminate one variable , we need to make the coefficients of one variable equal in both the equations.

Let us choose to eliminate the variable x.

Multiplying (2) by 2 [because 2 is the coefficient of x in the first equation]gives us  2x + 14y = 18 ----------------------(3)
          2x + 3y = 7----------------------(1)

Once we subtract these two equations, we get..
             14y - 3y = 18 - 9
==>              11y = 11  [An equation in 1 variable]
==>                y = 1  [dividing by 11 both the sides]

Now we have the value of 1 variable y = 1.

Now plug in this value of y in any of the above three equations to arrive at the value of x.

Let us substitute y = 1 in eqn(1)
==> 2x + 3(1) = 7
==> 2x + 3 = 7
==> 2x = 4 [subtracting 3 from both the sides of the equation]
==> x = 2 [dividing both the sides of the equation by 2]

Thus we have solved the given equations arriving (x,y) as (2,1).
We could plug in these values in the given equations to check if we have worked it out right.

Steps to be followed:
1> Choose to eliminate one variable
2> Make the coefficients of that variable equal in both the equations.[by multiplying]
3> Add or subtract to cancel them.
4> solve the resulting equation for 1 variable.
5> plug in this in one of the equations to arrive at the value of the other variable.

Hope it is clear to you.

Good Luck!!!