X + 9y = 24 3x + 4y = 3 What is the system of equations by using the substitution method?

Given the equations:

x + 9y = 24

3x + 4y = 3

Determine the systems of equation using the substitution method.

Solution:

Choose one equation and solve for y, in our case we'll choose equation 1.

x + 9y = 24

Transpose x on the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.

9y = 24 - x

Divide both sides by 9 in order to cancel out  9y, leaving behind y.

9y/9 = (24 - x )/9

y = 24/9 - 1/9 x

y = 7/3 - 1/9x

Susbtitute the value of y to the 2nd equation.

3x + 4 (7/3 - 1/9x)  = 3

3x + 28/3 - 4/9x  =3

Combine like terms.

3x can be written as  27/9 to easily combine with 4/9x, while 3 can be written as 9/3 to easily combine with 28/3

27/9x  - 4/9x + 28/3 - 9/3 = 0

23/9x - 19/3 = 0

In order to  determine the value of x, transpose -19/3 on the other side of the equation, and then multiply both sides by 9/23 to cancel out 23/9x.

(9/23) (23/9x) = 19/3 (9/23)

x = 171/ 69

Final answer:

23/9x - 19/3 = 0

x = 171/ 69