Question

1. graph the system of equations, and then estimate the solution.

$y = 2x + 4$
$y = -x - 3.5$

Explanation:

Step1: Find intersection algebraically

Set equations equal: $2x + 4 = -x - 3.5$

Step2: Solve for x

$2x + x = -3.5 - 4$
$3x = -7.5$
$x = \frac{-7.5}{3} = -2.5$

Step3: Find y with x=-2.5

Substitute into $y=2x+4$:
$y = 2(-2.5) + 4 = -5 + 4 = -1$

Step4: Verify with second equation

$y = -(-2.5) - 3.5 = 2.5 - 3.5 = -1$

Answer:

The solution (intersection point) is $(-2.5, -1)$

To graph:

1. For $y=2x+4$: plot y-intercept $(0,4)$, use slope 2 to plot $(1,6)$ and $(-1,2)$, draw line.
2. For $y=-x-3.5$: plot y-intercept $(0,-3.5)$, use slope -1 to plot $(1,-4.5)$ and $(-1,-2.5)$, draw line.

The lines cross at $(-2.5, -1)$.