Final answer:
To solve the system of equations y=4x-1 and y=2x+9 using substitution, set the right-hand sides equal to each other to find x=5. Subsequently, substitute x into either equation to find y=19, yielding the solution (5, 19).
Step-by-step explanation:
The student is asking how to solve a system of linear equations using substitution. Specifically, they have provided the equations y=4x-1 and y=2x+9. To use substitution, we first recognize that both equations equal y. We can set the right-hand sides of the equations equal to each other, resulting in 4x - 1 = 2x + 9. From here, we solve for x by subtracting 2x from both sides and adding 1 to both sides, yielding 2x = 10. Dividing by 2, we find that x = 5. After finding the value of x, we substitute it back into either of the original equations to find y. Using the first equation, we get y = 4(5) - 1, so y = 19. The solution to the system of equations is the point (5, 19).