3⁄4x - y = 2
1⁄8x + 1⁄4y = 2
Lets convert the coefficients to whole numbers - integers by multiplying each equation by 8
6x - 8y = 16
x + 2y = 16
We now want either the coefficient of x or coefficient of y to be the same. Lets choose the coefficient of x to be both 6. We will need to multiply the secondary equation by 6
6x - 8y = 16
6x + 12y = 96
Now we can subtract the first equation from the second
20y = 80
We just have one equation with one unknown variable. We can see that y = 4
Finally we need to find x so choose any of the original equations. I will choose the second equation since the coefficients are small numbers
x + 2y = 16
Finally substitute y = 4 to find the x value
x = 8
The final solution is therefore x = 8 and y = 4
6x - 8y = 16
x + 2y = 16
You may have prefered to have the y coefficients the same so we will multiply the second equation by 4
6x - 8y = 16
4x + 8y = 64
Since the signs are different, if we subtract one equation from the other we will still have two unknown variables. In this case we should add the equations.
10x = 80
Solving this equation we can see that x is 8. We can also substitute the x = 8 into any of the original equations and will find again that y = 4
The final solution is therefore x = 8 and y = 4
6x - 8y = 16
x + 2y = 16
First we can find an expression for x in terms (or y in terms of x). Then substitution that expression in the other equation. I will express x in terms of y since there are less steps.
x = 16 - 2y
Now I will substitute this expression into the first equation.
6(16-2y) - 8y = 16
We can expand and simplify
96 - 20y = 16
Solving this equation we can see that y = 4
Finally substitute y =4 into any of the original equations to find x. I am going to choose the second equation because the coefficients are smaller
x + 2(4) = 16
We see that x = 8 and also y =4