Question

A system of equations is shown below.What is the largest value of y in the solution set of the system?

Answer 1

Given

`\begin{gathered} y=x^2+2x+4 \\ y=-x+4 \end{gathered}`

To find the largest value of y in the solution set.

Step-by-step explanation:

It is given that,

`\begin{gathered} y=x^2+2x+4 \\ y=-x+4 \end{gathered}`

Then,

`\begin{gathered} -x+4=x^2+2x+4 \\ -x=x^2+2x \\ x^2+2x+x=0 \\ x^2+3x=0 \\ x(x+3)=0 \\ x=0,x+3=0 \\ x=0,x=-3 \end{gathered}`

Therefore, the solution set is {-3,0}.

That implies, the value of y in the solution set of the system is,

`\begin{gathered} For\text{ }x=0, \\ y=-(0)+4 \\ y=4 \\ For\text{ }x=-3, \\ y=-(-3)+4 \\ y=3+4 \\ y=7 \end{gathered}`

Hence, the largest value of y in the solution set of the system is option d) 7.