Solve the following pair of equations:49x + 51y = 49951x + 49 y = 501

To solve the given pair of equations:

Step 1: Write the equations in standard form: 49x + 51y = 499 51x + 49y = 501

Step 2: Multiply the first equation by 51 and the second equation by 49 to eliminate the coefficients of x: (49x + 51y) * 51 = 499 * 51 (51x + 49y) * 49 = 501 * 49

This simplifies to: 2499x + 2601y = 25449 2499x + 2401y = 24549

Step 3: Subtract the second equation from the first equation to eliminate x: (2499x + 2601y) - (2499x + 2401y) = 25449 - 24549

Simplifying further: 200y = 900

Step 4: Solve for y by dividing both sides of the equation by 200: y = 900 / 200 y = 4.5

Step 5: 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

Simplifying: 49x + 229.5 = 499 49x = 499 - 229.5 49x = 269.5

Step 6: Solve for x by dividing both sides of the equation by 49: x = 269.5 / 49 x ≈ 5.5

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