Question

uations graphically on the set of axes below. y = -2x - 4 y = x + 2

Explanation:

Step1: Find the y - intercepts

For \(y=-2x - 4\), when \(x = 0\), \(y=-4\). For \(y=x + 2\), when \(x = 0\), \(y=2\).

Step2: Find the x - intercepts

For \(y=-2x - 4\), set \(y = 0\), then \(0=-2x-4\), \(2x=-4\), \(x=-2\). For \(y=x + 2\), set \(y = 0\), then \(0=x + 2\), \(x=-2\).

Step3: Plot the lines

Plot the points \((0,-4)\) and \((-2,0)\) for \(y=-2x - 4\) and connect them with a straight - line. Plot the points \((0,2)\) and \((-2,0)\) for \(y=x + 2\) and connect them with a straight - line. The intersection point of the two lines is the solution of the system of equations.
To find the intersection point algebraically:
Set \(-2x-4=x + 2\).
Add \(2x\) to both sides: \(-4=x + 2+2x\), \(-4=3x + 2\).
Subtract 2 from both sides: \(-4-2=3x\), \(-6=3x\).
Divide both sides by 3: \(x=-2\).
Substitute \(x=-2\) into \(y=x + 2\), \(y=-2 + 2=0\).

Answer:

The intersection point of the two lines \(y=-2x - 4\) and \(y=x + 2\) is \((-2,0)\) which is the solution of the system of equations.