Question

(HELP ASAP)

Use substitution or elimination to find the solutions to the system.
y = x² +7x+8
y=x+3​

Answer 1

`\sf (-5, -2)` and
`\sf (-1, 2)`

Explanation:

Let's use substitution to find the solutions to the system. The system is:

1.
`\sf y = x^2 + 7x + 8`

2.
`\sf y = x + 3`

Since both expressions are equal to
`\sf y`, we can set them equal to each other:

`\sf x^2 + 7x + 8 = x + 3`

Now, let's rearrange the equation and set it to zero:

`\sf x^2 + 6x + 5 = 0`

Now, doing middle term factorization to the quadratic:

`\sf x^2 + (5+1)x + 5 = 0`

`\sf x^2 + 5x + 1x + 5 = 0`

`\sf x(x+5)+1(x+5) = 0`

`\sf (x + 5)(x + 1) = 0`

This gives two possible solutions:

1.
`\sf x + 5 = 0`
`\sf \Rightarrow`
`\sf x = -5`

2.
`\sf x + 1 = 0`
`\sf \Rightarrow`
`\sf x = -1`

Now that we have the values of
`\sf x`, we can substitute them back into either of the original equations to find the corresponding
`\sf y` values.

Let's use the second equation for this:

For
`\sf x = -5`:

`\sf y = (-5) + 3 = -2`

For
`\sf x = -1`:

`\sf y = (-1) + 3 = 2`

Therefore, the solutions to the system are
`\sf (-5, -2)` and
`\sf (-1, 2)`.