Question

solve graphically: y = x\
y + 2 = x

Explanation:

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

The equation \( y = x \) is a linear equation with a slope of \( 1 \) and a \( y \)-intercept of \( 0 \). To graph it, we can find two points. When \( x = 0 \), \( y = 0 \), so the point \( (0,0) \) is on the line. When \( x = 1 \), \( y = 1 \), so the point \( (1,1) \) is also on the line. We can draw a straight line through these two points.

Step2: Analyze the second equation \( y + 2 = x \)

Rewrite the second equation in slope - intercept form (\( y=mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept). Solving \( y + 2=x \) for \( y \), we get \( y=x - 2 \). The slope of this line is \( 1 \) and the \( y \)-intercept is \( - 2 \). To graph it, when \( x = 0 \), \( y=-2 \), so the point \( (0, - 2) \) is on the line. When \( x = 2 \), \( y=2 - 2=0 \), so the point \( (2,0) \) is on the line. We can draw a straight line through these two points.

Step3: Determine the intersection of the two lines

The first line \( y = x \) has a slope of \( 1 \) and \( y \)-intercept \( 0 \). The second line \( y=x - 2 \) has a slope of \( 1 \) and \( y \)-intercept \( - 2 \). Since the slopes of the two lines are equal (\( m_1=m_2 = 1 \)) and the \( y \)-intercepts are different (\( b_1 = 0
eq b_2=-2 \)), the two lines are parallel. Parallel lines do not intersect, so there is no solution to the system of equations.

Answer:

There is no solution (the two lines are parallel and do not intersect).