Final answer:
To find the value of x when two lines meet at a point, use slope-intercept form and equate the equations. For three lines, use simultaneous equations. For two lines meeting at the endpoint of two rays, use simultaneous equations.
Step-by-step explanation:
Question 1
To set up and solve an equation to find the value of x when two lines meet at a point, you need to use the concept of slope-intercept form. The equation of each line will be in the form y = mx + b, where m represents the slope and b represents the y-intercept. Equate the two equations to find the value of x, which represents the point of intersection.
Line 1: y = 2x + 3
Line 2: y = -3x + 4
Equate the two equations: 2x + 3 = -3x + 4
Solve the equation for x: 5x = 1 ⟹ x = 1/5
Question 2
To set up and solve an equation to find the value of a when three lines meet, you need to use the concept of simultaneous equations. Each equation will represent a line, and equating them will give you a system of equations. Solve the system to find the value of a. The answer can be checked for reasonableness by evaluating if the solution satisfies each equation in the system.
Question 3
To set up and solve an equation to find the values of a and b when two lines meet at a point that is also the endpoint of two rays, you need to use the concept of simultaneous equations again. Each equation will represent a line, and equating them will give you a system of equations. Solve the system to find the values of a and b.