5x-4y=10

2x+8y=4

rewrite #1 and you get

10x-8y=20
2x+8y=4

Now add the two equations and y goes away. Solve for x, then get y.

Thanks Steve.

But how???

Please explain it.

If you add the two equations, you get

12x = 24

because -8y+8y = 0

Now you know x=2, so y=0

To solve this system of equations, you can use either the substitution method or the elimination method. Let's use the elimination method to find the values of x and y.

Step 1: Multiply the first equation by 2 and the second equation by 5 in order to eliminate the x term.

Original equations:
5x - 4y = 10
2x + 8y = 4

Modified equations:
10x - 8y = 20
10x + 40y = 20

Step 2: Now, subtract the two modified equations to eliminate the x term.

(10x - 8y) - (10x + 40y) = 20 - 20
-8y - 40y = 0
-48y = 0

Step 3: Solve for y.

-48y = 0
y = 0

Step 4: Substitute the value of y (y = 0) back into one of the original equations to find the value of x. Let's use the first equation.

5x - 4(0) = 10
5x = 10
x = 2

Therefore, the solution to the system of equations is x = 2 and y = 0.