To find the solution to the system of equations:
5x + 4y = 8
10x - 4y = 46
We can use the method of elimination to eliminate one variable and solve for the other.
First, let's multiply the second equation by 2 to make the coefficients of y's in both equations opposites:
2(10x - 4y) = 2(46)
20x - 8y = 92
Now, we can add the two equations together to eliminate y:
(5x + 4y) + (20x - 8y) = 8 + 92
(5x + 20x) + (4y - 8y) = 100
25x - 4y = 100
Now we have a new equation:
25x - 4y = 100
Next, let's eliminate y by multiplying the first equation by 4:
4(5x + 4y) = 4(8)
20x + 16y = 32
Now, let's add this equation to the previous one:
(20x + 16y) + (25x - 4y) = 32 + 100
(20x + 25x) + (16y - 4y) = 132
45x + 12y = 132
Now we have another new equation:
45x + 12y = 132
We now have a system of two equations:
25x - 4y = 100
45x + 12y = 132
Solving this system of equations, we will find the values of x and y.