Question

solve this system of equations by graphing. first graph the equations, and then type the solution.

$y = -x - 7$

$y = -4$

click to select points on the graph.

graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and two buttons at the bottom: green with $y = -x - 7$ and blue with $y = -4$

Explanation:

Step1: Analyze \( y = -4 \)

The equation \( y = -4 \) is a horizontal line. All points on this line have a \( y \)-coordinate of \(-4\). So we can plot points like \((0, -4)\), \((2, -4)\), \((-2, -4)\) etc.

Step2: Analyze \( y = -x - 7 \)

This is a linear equation in slope - intercept form \( y=mx + b\), where the slope \( m=- 1\) and the \( y \)-intercept \( b = - 7\). To graph it, we can find two points. When \( x = 0\), \( y=-0 - 7=-7\), so we have the point \((0,-7)\). When \( y = 0\), \(0=-x - 7\), which gives \(x=-7\), so we have the point \((-7,0)\). We can also use the fact that we know \( y=-4\) from the other equation. Substitute \( y = - 4\) into \( y=-x - 7\):

$$
LATEXBLOCK0
$$

Step3: Find the intersection

The solution to the system of equations is the point where the two lines intersect. From the above calculation, when \( y=-4\), \(x = - 3\). So the intersection point is \((-3,-4)\).

Answer:

The solution to the system of equations is \((-3, - 4)\)