Question

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)?

Answer 1

To find out if the points are solutions to the system of equation, we need to substitute them in the equations and perform the needed calculation to check if it is a solution:

`\begin{gathered} (-4.8,41.4) \\ 2(-4.8)^2=41.4+5 \\ 2*23.04=46.4 \\ 46.08=46.4 \end{gathered}`

Using the same point for the line equation, we have,

`\begin{gathered} y=-8x+3\to41.4=-8*(-4.8)+3 \\ 41.4=38.4+3 \\ 41.4=41.4 \end{gathered}`

The first point is a solution only for the linear equation, not for the quadratic one.

Now, let's substitute the second point (0.8, -3.4) in the quadratic equation:

`\begin{gathered} 2*(0.8)^2=-3.4+5 \\ 2*0.64=1.6 \\ 1.28=1.6 \end{gathered}`

Now, let us check if the second point is for the line equation:

`\begin{gathered} -3.4=-8*(0.8)+3 \\ -3.4=-6.4+3 \\ -3.4=-3.4 \end{gathered}`

From the solution developed above, we are able to conclude that both points are solutions for the line equation, but not for the quadratic one.

From this, we can also say that the correct answer is NO. The points are solutions only for the line.