Final answer:
The point of intersection between the two equations y=5x-8 and y=-2x-35 is (-3, -23).
Step-by-step explanation:
To find the point of intersection between the two equations, y=5x-8 and y=-2x-35, we need to set the two equations equal to each other and solve for x. So, we have 5x-8=-2x-35. Adding 2x to both sides gives us 7x-8=-35. Adding 8 to both sides gives us 7x=-27. Finally, dividing both sides by 7 gives us x=-3.
To find the y-coordinate of the point of intersection, we can substitute the value of x we just found back into either of the original equations. Substituting x=-3 into y=5x-8 gives us y=5(-3)-8, which simplifies to y=-15-8=-23.
Therefore, the point of intersection between the two equations is (-3, -23).