Question

The point (3,-1)( 3 , − 1 ) is a solution to this system of equations:

Answer 1

The system of equations we have is:

`\begin{gathered} -3x-2y=-7 \\ x+4y=1 \end{gathered}`

And we need to check if the point (3,-1) is a solution.

Step 1. Identify the values of x and y from the point.

In a point, the first number represents the x-value, and the second number represents the y-value. So in point (3,-1) 3 is the x-value, and -1 is the y-value:

`\begin{gathered} x=3 \\ y=-1 \end{gathered}`

Step 2. Substitute the x and y-value into the first equation and check that the result is equal to -7.

The first equation is:

`-3x-2y=-7`

Substituting x=3 and y=-1:

`-3(3)-2(-1)=`

Solve the operations:

`-9+2=-7`

Since we get -7 as the result, (3,-1) is a solution for the first equation. But we still need to check if the point is a solution for the second equation.

Step 3. Substitute the x and y values into the second equation and check that the result is 1.

The second equation of the system is:

`x+4y=1`

Substituting x=3 and y=-1:

`3+4(-1)=`

Solving the operations:

`3-4=-1`

The result we get is -1, not 1. Thus, since the point (3,-1) is not a solution for the second equation, it is also not a solution to the system of equation.

Answer: False