Question

Solve this system using substitution method...show work

Answer 1

The given SYSTEM OF EQUATION HAS NO SOLUTION.

Explanation:

Here, the given system of equations are:

`x = 4y + 3\\2y - (1)/(2) x = 9`

Solving the system by substitution:

Substitute the value of x = 4y + 3 in the second equation, we get
`2y - (1)/(2) x = 9 \implies 2y - (1)/(2) (4y+3) = 9\\\implies 2y - (1)/(2) (4y) -(1)/(2) (3)  = 9\\\implies 2y - 2y -(3)/(2)   = 9\\or, 0 = 9+(3)/(2)  = (21)/(2)`

⇒ 0 = 21/2

This gives us a CONTRADICTION as 0 ≠21/2

Hence, the above SYSTEM HAS NO SOLUTION.