Given: The system of equations:
[tex]\begin{gathered} y=-3x+5 \\ 6x+2y=10 \end{gathered}[/tex]Required: Check whether the given order pair are solution to the system of equation or not.
(-2, 11)
(4,-7)
(0,4)
(-3,-6)
Explanation:
The equations are
[tex]\begin{gathered} 3x+y=5 \\ 6x+2y=10 \end{gathered}[/tex]These are actually the same equations and solution to these two equations are infinite.
So we check solution for first equation only.
Any orderd pair is a solution, if it satisfies the equation.
(1) Put (-2,11) in equation 3x+y=5
[tex]\begin{gathered} 3(-2)+11=5 \\ -6+11=5 \end{gathered}[/tex]which is true. Hence, (-2,11) is a solution.
(2) Put (4,-7) in equation
[tex]3(4)-7=12-7=5[/tex]which is correct. Hence (4,-7) is a solution.
(3) Put (0,4) in the equation
[tex]3(0)+4=0+4=4\ne5[/tex]Hence, (0,4) is not a solution.
(4) Put (-3,-6) in the equation.
[tex]3(-3)-6=-9-6=-15\ne5[/tex]Hence, (-3,-6) is not a solution.
Final Answer: (-2,11) and (4,-7) are solution to system of equation, whereas (0,4) and (-3,-6) are not.
