49x + 51y = 49951x + 49 y = 501

To solve the system of equations:

49x + 51y = 499 51x + 49y = 501

Step 1: Multiply the first equation by 51 and the second equation by 49 to eliminate the y terms.

(49x + 51y) * 51 = 499 * 51 (51x + 49y) * 49 = 501 * 49

Simplifying, we get:

2499x + 2601y = 25449 2499x + 2401y = 24549

Step 2: Subtract the second equation from the first equation to eliminate the x terms.

(2499x + 2601y) - (2499x + 2401y) = 25449 - 24549

Simplifying, we get:

200y = 900

Step 3: Divide both sides of the equation by 200 to solve for y.

y = 900 / 200 y = 4.5

Step 4: Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation.

49x + 51(4.5) = 499 49x + 229.5 = 499

Step 5: Subtract 229.5 from both sides of the equation.

49x = 499 - 229.5 49x = 269.5

Step 6: Divide both sides of the equation by 49 to solve for x.

x = 269.5 / 49 x = 5.5

Therefore, the solution to the system of equations is x = 5.5 and y = 4.5.