Using the elimination method simply means finding numbers in common in order to cancel out to find the unknown variable for this step we notice that we were told to find x and y so first to find y you have to get rid of x since in simple algebra we understand the positive and negative attract and cancel each other out we use the negative value for x and multiply it for the first unknown value in order to cancel x as seen in the problem below.
-7(7x+2y =19)
7(7x+8y=13)
When we worked out the multiplications and have done our cancellation what we are left with will be y. Therefore leading us to the final answer
49x-14y= -133
-49x+56y=91
Here since the value for which we are looking for is y and we see a different variable or number beside it we use that number to divide both sides in prefer to find the value of y
42y=42
42y/42= 42/42
Y=1
Therefore, y value is 1. Now knowing that y=1 we can now use the substitution method to find x value by using only one of these equations but this is just the scrape value of y it’s not real for each we’ll use one to find each value.
7x+2y =19
7x+8y =13
Using 7x+8y=13 to find x first
7x+8y=13
7x+8(1)=13
7x+8=13
In algebra we were taught to transpose if not then here are the steps
1. Whatever variable you want to transpose it has to cancel from both sides meaning whatever you add to the left side it should be on the right side as well
7x+8-8=13-8
Therefore,
7x= 13-8
7x= 5
7x/7= 5/7
x= 0.714 or just 1.0.
Now Using,
7x+2y =19
7(0.714)+2y=19
4.998+2y=19
Round 4.998 to 5.0
5-5+2y=19-5
2y=14
2y/2=14/2
Y=7.
Now X value is 1 and Y value is 7. If you want to check you can use the first two equation substituting x for the value of x and y for the value of Y.