Question

A system of equations is shown; and . What is the smallest = 2 + 3 − 5 = + 3valueof in the solution set of the system?

Answer 1

Option B

Step-by-step explanation:

Given that:

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

Since the right hand side of both equations are same, equate the left hand side of both the equations.

`\begin{gathered} x^2+3x-5=x+3 \\ x^2+2x-8=0 \\ (x+4)(x-2)=0 \\ x=-4,2 \end{gathered}`

The values of x are -4 and 2.

Substitute the values of x into the equation y = x+3.

When x = -4,

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

When x = 2,

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

y takes the values -1 and 5. Since -1 is less than 5, the smallest value of y is -1.

So, option B is correct.