Question

Algebraically solve the following system of equations. Show all of the work: 2x+5y=33x-2y=14

Answer 1

From the given equation

`\begin{gathered} 2x+5y=3\ldots(1) \\ 3x-2y=14\ldots(2) \end{gathered}`

Now,

from the equation (1)

`\begin{gathered} 2x+5y=3 \\ 2x=3-5y \\ x=(1)/(2)(3-5y)\ldots(3) \end{gathered}`

Then,

Put the value of x into the equation (2)

`\begin{gathered} 3x-2y=14 \\ 3((3)/(2)-(5)/(2)y)-2y=14 \\ (9)/(2)-(15)/(2)y-2y=14 \\ 9-15y-4y=28 \\ 9-19y=28 \\ -19y=28-9 \\ -19y=19 \\ y=-1 \end{gathered}`

Then,

Put the value of y into the equation (3)

So,

`\begin{gathered} x=(1)/(2)(3-5y) \\ x=(1)/(2)(3-5(-1)) \\ x=(1)/(2)(3+5) \\ x=(8)/(2) \\ x=4 \end{gathered}`

Hence, the value of x is 4 and y is -1.