Question 632979
4x-y=5
9x-2y=13


4x - y = 5 (1)

9x - 2y = 13 (2)

Let's take the first equation:

4x - y = 5

Add y to each side of the equation.

4x - y + y = 5 + y

Combine like terms:

-y + y = 0


Therefore:

4x = 5 + y

Divide each side by 4

4x/x = (5 + y)/4

x = (5 + y)/4


Substitute x = (5 + y)/4 into the second equation:

9x - 2y = 13

9(5 + y)/4 - 2y = 13

Multiply each item above by 4

9(5 + y)/4 * 4 - 2y * 4 = 13 * 4

9(5 + y)/4 * 4 = 9(5 + y)

9 * 5 = 45

9 * y = 9y

-2y * 4 = -8y

13 * 4 = 52


Therefore:

45 + 9y - 8y = 52

Combine like terms:

9y - 8y = 1y

45 - 1y = 52

Subtract 45 from each side of the equation.

45 - 1y - 45 = 52 - 45

Combine like terms:

45 - 45 = 0

52 - 45 = 7

1y = 7 or

y = 7


Substitute y = 7 into equation 1

4x - y = 5

4x - 7 = 5

Add 7 to each side of the equation.

4x - 7 + 7 = 5 + 7

Combine like terms:

-7 + 7 = 0

5 + 7 = 12

4x = 12

Divide each side by 4

4x/4 = 12/4

x = 3


The Answer:

x = 3

y = 7




Lennox Obuong
Algebra Student
Email: obuong3@aol.com