Answer :
(-7, 2)
STEP - BY - STEP EXPLANATION
What to find?
The solution to the given the system of equations .
Given:
[tex]\begin{gathered} -\frac{5}{4}x-\frac{5}{4}y=\frac{25}{4} \\ \\ \frac{1}{5}x+\frac{4}{5}y=\frac{1}{5} \end{gathered}[/tex]To solve the above system of equations, we will follow the steps below:
Step 1:
Multiply through equation (1) by 4
[tex]-5x-5y=25\text{ ----------------------(2)}[/tex]Step 2
Multiply through the second equation by 5.
[tex]x+4y=1\text{ -------------------------(3)}[/tex]Step 3
Using substitution method to solve.
Make x the subject of formular.
[tex]x=1-4y-------------------(4)[/tex]Step 4
Substitute equation(4) into equation (2).
[tex]-5(1-4y)-5y=25[/tex]Step 5
Open the parenthesis.
[tex]-5+20y-5y=25[/tex]Step 6
Collect like term.
[tex]\begin{gathered} 20y-5y=25+5 \\ 15y=30 \end{gathered}[/tex]Step 7
Divide both-side of the equation by 15.
[tex]\begin{gathered} \frac{15y}{15}=\frac{30}{15} \\ \\ y=2 \end{gathered}[/tex]Step 8
Substitute y=2 into equation (4) to determine the value of x.
[tex]\begin{gathered} x=1-4(2) \\ =1-8 \\ =-7 \end{gathered}[/tex]Hence, x =-7 and y=2.
Therefore, the solution in ordered pair is (-7, 2)
