Question

For each ordered pair, determine whether it is a solution to the system of equations.y=-3x+56x+2y=10Is it a solution?YesNo(x, y)(-2, 11)(4,-7)(0,4)(-3,-6)

Answer 1

Given: The system of equations:

`\begin{gathered} y=-3x+5 \\ 6x+2y=10 \end{gathered}`

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

`\begin{gathered} 3x+y=5 \\ 6x+2y=10 \end{gathered}`

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

`\begin{gathered} 3(-2)+11=5 \\ -6+11=5 \end{gathered}`

which is true. Hence, (-2,11) is a solution.

(2) Put (4,-7) in equation

`3(4)-7=12-7=5`

which is correct. Hence (4,-7) is a solution.

(3) Put (0,4) in the equation

`3(0)+4=0+4=4\\e5`

Hence, (0,4) is not a solution.

(4) Put (-3,-6) in the equation.

`3(-3)-6=-9-6=-15\\e5`

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.