Question

Choose the correct graph of the given systems of equations.

y-2x = -1
2y - x = 4
Select one:
O a.
O b.
a
(0, -1) One Solution
b
(2,3) One Solution
P

Answer 1

The correct graph for the system of equations y - 2x = -1 and 2y - x = 4 is the one showing the intersection point at (2, 3). By solving the equations, we find that this point is the solution to the system, matching graph b.

Step-by-step explanation:

To choose the correct graph for the system of equations y - 2x = -1 and 2y - x = 4, we need to first solve the equations to find the point of intersection, which will represent the solution to the system of equations.

Step-by-step solution:

1. Rewrite the first equation in slope-intercept form (y = mx + b):
   y = 2x - 1.
2. Rewrite the second equation in slope-intercept form:
   2y = x + 4
   y = (1/2)x + 2.
3. Set the two equations equal to each other to find the x-coordinate of the intersection:
   2x - 1 = (1/2)x + 2.
4. Solve the above equation for x:
   2x - (1/2)x = 2 + 1
   (3/2)x = 3
   x = 2.
5. Substitute x = 2 into one of the original equations to find y:
   y = 2(2) - 1
   y = 3.
6. The solution to the system is (2, 3), so the correct graph must have these coordinates as the point of intersection.

Based on the solution, graph b is correct because it shows the point of intersection (2, 3) which is the one solution to the system.