Question

excellent observation! youre looking at the graph and identifying where the lines intersect. thats exactly the right thinking process!
now let me guide you to verify this answer. you said the solution is (-2, 0). heres how we can check if this is correct:
lets test this point in both equations:
for the point (-2, 0) to be the solution, it must satisfy both equations:

• ( y = -2x - 4 )
• ( y = 2x + 4 )

can you substitute x = -2 and y = 0 into the first equation and see what you get?
start with: ( y = -2x - 4 ) if x = -2 and y = 0, does this equation work out to be true?
try it and tell me what you find. then well check the second equation too.
this is a great way to verify any solution - by substituting the coordinates back into both original equations!

Explanation:

Step1: Substitute into the first equation

Substitute \(x = - 2\) and \(y = 0\) into \(y=-2x - 4\).
Left - hand side (LHS): \(y = 0\)
Right - hand side (RHS): \(-2\times(-2)-4\)

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Since \(LHS = RHS\) (i.e., \(0 = 0\)), the point \((-2,0)\) satisfies the first equation \(y=-2x - 4\).

Step2: Substitute into the second equation

Substitute \(x=-2\) and \(y = 0\) into \(y = 2x+4\).
Left - hand side (LHS): \(y = 0\)
Right - hand side (RHS): \(2\times(-2)+4\)

$$
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Since \(LHS=RHS\) (i.e., \(0 = 0\)), the point \((-2,0)\) satisfies the second equation \(y = 2x + 4\).

Answer:

The point \((-2,0)\) is the solution of the system of equations \(y=-2x - 4\) and \(y = 2x+4\) because it satisfies both equations.