Final answer:
To find the point of intersection of each pair of lines, solve the system of equations formed by the given pairs. A.) (-5, 1), B.) (3, 1), C.) No point of intersection.
Step-by-step explanation:
To find the point of intersection of each pair of lines, we need to solve the system of equations formed by the given pairs. Let's go through each pair one by one:
A.) x= -2y-3 and 4y-x=9
Solving the first equation for x, we get x = -2y-3. Substituting this value of x into the second equation, we get 4y - (-2y-3) = 9. Simplifying this equation, we get 4y + 2y + 3 = 9 which further simplifies to 6y + 3 = 9. Solving for y, we get y = 1. Substituting this value of y into the first equation, we get x = -2(1) - 3 = -5. Therefore, the point of intersection for this pair of lines is (-5, 1).
B.) x+5y=8 and -x+2y=-1
Adding both equations together, we get (x + 5y) + (-x + 2y) = 8 + (-1). Simplifying this equation, we get 7y = 7 which gives y = 1. Substituting this value of y into either of the two original equations, we get x + 5(1) = 8 which simplifies to x + 5 = 8, leading to x = 3. Therefore, the point of intersection for this pair of lines is (3, 1).
C.) 4x-2y=-1 and y=2x+10
Substituting the value of y from the second equation into the first equation, we get 4x - 2(2x+10) = -1. Simplifying this equation, we get 4x - 4x - 20 = -1 which simplifies to -20 = -1 - which is not a valid equation. Therefore, this pair of lines does not have a point of intersection.