Question

Solve the following pairs of equations by reducing them to a pair of linear equations. Solve for (X) and (Y):

(5x + 4y = 9)
(7x - 2y = 5)
(Note: (Y) is not equal to zero)
a) (X = 1, Y = 43)
b) (X = 32, Y = 2)
c) (X = -2, Y = -12)
d) (X = 0, Y = 1)

Answer 1

To find the values of X and Y, we used the elimination method, where we manipulated the equations 5x + 4y = 9 and 7x - 2y = 5 to solve for X and Y. The correct values we found are X = 1 and Y = 1, which do not match any of the offered options.

Step-by-step explanation:

To solve the pair of equations 5x + 4y = 9 and 7x - 2y = 5, we will use the method of substitution or elimination. Let's solve them using elimination. We need to make the coefficients of y the same in both equations so that they cancel each other out when we add or subtract the equations.

First, multiply the first equation by 2 and the second equation by 4 to get:

• 
  
• 
  

Now add both equations:

10x + 8y + 28x - 8y = 18 + 20

38x = 38

Divide both sides by 38 to find x:

x = 1

Now substitute x = 1 into one of the original equations to find y:

5(1) + 4y = 9

5 + 4y = 9

4y = 9 - 5

4y = 4

Divide both sides by 4 to find y:

y = 1

The solution to the system of equations is X = 1 and Y = 1, which is not listed among the given options, suggesting that all provided options are incorrect.