Final answer:
To solve the system of equations, we set up the two equations y = x + 250 and x + y = 1400. Applying substitution, we find that x = 575 and y = 825. Therefore, the cost of the dryer is $575 and the cost of the washer is $825.
Step-by-step explanation:
To solve this problem, we can set up a system of two linear equations. Let's define the cost of the dryer as x and the cost of the washer as y. Given that the washer costs $250 more than the dryer, we can set up the equation: y = x + 250. We also know that the total cost of the washer-dryer combination is $1400, so we can set up the second equation: x + y = 1400.
To solve this system of equations, we can use substitution or elimination. Let's use substitution in this case. We already have the equation y = x + 250, so we can substitute this value into the second equation: x + (x + 250) = 1400.
Simplifying the equation, we have 2x + 250 = 1400. Subtracting 250 from both sides gives us 2x = 1150. Dividing both sides by 2, we find that x = 575.
Therefore, the cost of the dryer is $575. To find the cost of the washer, we can substitute this value back into one of the original equations. Using y = x + 250, we have y = 575 + 250, which gives us y = 825. So, the cost of the washer is $825.