Question

Solve the system of equations and wright your answer as an ordered pair -5/4x-5/4y =25/41/5x+4/5y=1/5

Answer 1

(-7, 2)

STEP - BY - STEP EXPLANATION

What to find?

The solution to the given the system of equations .

Given:

`\begin{gathered} -(5)/(4)x-(5)/(4)y=(25)/(4) \\ \\ (1)/(5)x+(4)/(5)y=(1)/(5) \end{gathered}`

To solve the above system of equations, we will follow the steps below:

Step 1:

Multiply through equation (1) by 4

`-5x-5y=25\text{ ----------------------(2)}`

Step 2

Multiply through the second equation by 5.

`x+4y=1\text{ -------------------------(3)}`

Step 3

Using substitution method to solve.

Make x the subject of formular.

`x=1-4y-------------------(4)`

Step 4

Substitute equation(4) into equation (2).

`-5(1-4y)-5y=25`

Step 5

Open the parenthesis.

`-5+20y-5y=25`

Step 6

Collect like term.

`\begin{gathered} 20y-5y=25+5 \\ 15y=30 \end{gathered}`

Step 7

Divide both-side of the equation by 15.

`\begin{gathered} (15y)/(15)=(30)/(15) \\ \\ y=2 \end{gathered}`

Step 8

Substitute y=2 into equation (4) to determine the value of x.

`\begin{gathered} x=1-4(2) \\ =1-8 \\ =-7 \end{gathered}`

Hence, x =-7 and y=2.

Therefore, the solution in ordered pair is (-7, 2)