Question

What is the solution of the systems of equation?

\large 8x+5y=2

\large -2x+y=4

The solution is ( , )

Answer 1

The solution to the system of linear equations 8x+5y=2 and -2x+y=4 is found using the elimination method, resulting in the solution of (-1, 2).

Step-by-step explanation:

We're given a system of linear equations and asked to find the solution:

8x + 5y = 2
-2x + y = 4

To find the solution, we can use the method of substitution or elimination. For this example, let's use the elimination method:

1. Multiply the second equation by 5 to make the coefficients of y equal:
   -2x + y = 4
   
   5(-2x + y) = 5(4)
   -10x + 5y = 20
2. Now we subtract the new equation from the first one:
   8x + 5y = 2
   -(-10x + 5y = 20)
   
   The y terms cancel out, and we are left with 18x = -18.
3. Divide both sides by 18 to find x:
   x = -1.
4. Substitute x into the second original equation to find y:
   
   -2(-1) + y = 4
   
   2 + y = 4
   y = 2.

The solution to this system of equations is (x, y) = (-1, 2).