Final answer:
To find a pair of numbers that satisfies both equations -5y + x = 55 and -5y + 4x = 85, set the two equations equal to each other and solve for x. Substitute the value of x back into one of the original equations to solve for y. A pair of numbers that satisfies both equations is x = 10 and y = -5.
Step-by-step explanation:
To find a pair of numbers that satisfies both equations -5y + x = 55 and -5y + 4x = 85, we can set the two equations equal to each other and solve for x. So, -5y + x = -5y + 4x, which simplifies to x = 3x. We can then substitute the value of x back into one of the original equations to solve for y. Let's choose the first equation: -5y + (3x) = 55. Rearranging the equation gives us -5y = 55 - 3x. Now, we can plug in a value for x and solve for y. For example, if we choose x = 10, we have -5y = 55 - 3(10), which simplifies to -5y = 25. Dividing by -5 gives us y = -5. Therefore, a pair of numbers that satisfies both equations is x = 10 and y = -5.