Question

solve the following system of equations graphically on the set of axes below.
$y = x + 3$
$3x + y = -5$
plot two lines by clicking the graph.
click a line to delete it.
answer attempt 2 out of 2
solution: $(-2,1)$ submit answer

Explanation:

Step1: Analyze the first equation \( y = x + 3 \)

This is a linear equation in slope - intercept form \( y=mx + b \), where the slope \( m = 1 \) and the y - intercept \( b=3 \). To graph this line, we can find two points. When \( x = 0 \), \( y=0 + 3=3 \), so the point \( (0,3) \) is on the line. When \( x=-3 \), \( y=-3 + 3 = 0 \), so the point \( (-3,0) \) is on the line.

Step2: Analyze the second equation \( 3x + y=-5 \)

We can rewrite it in slope - intercept form \( y=-3x - 5 \). Here, the slope \( m=-3 \) and the y - intercept \( b = - 5 \). To find points on this line, when \( x = 0 \), \( y=-5 \), so the point \( (0,-5) \) is on the line. When \( x=-1 \), \( y=-3\times(-1)-5=3 - 5=-2 \), so the point \( (-1,-2) \) is on the line.

Step3: Find the intersection point

When we graph both lines, the point where they intersect is the solution to the system of equations. By looking at the graph (or by solving the system algebraically: substitute \( y=x + 3 \) into \( 3x + y=-5 \), we get \( 3x+(x + 3)=-5 \), \( 4x+3=-5 \), \( 4x=-8 \), \( x=-2 \), and then \( y=-2 + 3 = 1 \)), the intersection point is \( (-2,1) \).

Answer:

The solution to the system of equations is \( (-2,1) \)