Question

Y= 4x + 3 y= -x - 2 solve the system of linear equation by graphing

Answer 1

Answer:

(-1, -1)

Step-by-step explanation:

To solve a system of equations by graphing, first graph the lines. Then, find where the two lines hit each other. This is called the "point of intersection", which is the solution. Mark this point's coordinates as an ordered pair (x, y) for your answer.

The equations are in slope-intercept form y = mx + b.

"x" and "y" are points on the line.

"m" is the slope, which equals to $\frac{rise}{run}$.

"b" is the y-intercept, where a line hits the y-axis.

For y = 4x + 3 (blue):

b = 3. This first point is at "3", on the y-axis. Draw a dot there. Use the slope to get another point.

m = 4. Write it as a fraction to get the rise and run values.

$m=\frac{4}{1}$

From your first point, "rise" (go up) 4 squares, and "run" (go right) 1 squares. Put a dot here too.

Now, you can connect the two points to form a straight line. Remember to put arrows at the ends of the line.

For y = -x - 2 (red):

b = -2. This first point is at "-2", on the y-axis. Put a dot here.

Let's find the next point using the slope.

m = -1. Write it as a fraction to get the rise and run values.

$m=-\frac{1}{1}$

From your first point, "rise" -1 squares. This means to go down 1 square because the fraction is negative. "Run" (go right, same as before) 1 square. Draw your second point here.

Now, you can connect the two points to form a straight line. Remember to put arrows on the line again.

Extend the lines (keep making them longer) until they hit each other. Where they meet is the solution of the system.

The solution is (-1, -1).