Question

Determine whether the ordered pair is a solution to the given system of linear equations.
1.(5,3) \(\displaystyle{\left\lbrace\begin{array}{c} {x}-{y}={2}\\{x}+{y}={8}\end{array}\right.}\rbrace\)

Answer 1

Step 1
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Step 2
(1)
The given system of linear equations are
x−y=2 ...(1)
x+y=8 ...(2)
The given ordered pair for this system is (5, 3).
The ordered pair is the solution of the system it must be satisfy both the equations.
Step 3
Substitute x=5 and y=3 in the left side of the equation (1).
LHS=x-y
=5-3
=2
RHS
Substitute x=5 and y=3 in the left side of the equation (2).
LHS=x+y
=5+3
=8
=RHS
Since the ordered pair satisfies the system of linear equations.
Hence, the ordered pair (5, 3) is a solution to the given system of linear equations.