An unknown number y is 12 more than an unknown number x. The number y is also x less than 17. The equations to find x and y are shown below.
y = x + 12
y = −x + 17
Which of the following statements is a correct step to find x and y? (4 points)
A. Multiply the equations to eliminate y.
B. Write the points where the graphs of the equations intersect the x-axis.
C. Write the points where the graphs of the equations intersect the y-axis.
D. Add the equations to eliminate x.
D. Add the equations to eliminate x.
To find x and y, you can add the two equations together to eliminate x:
(x + 12) + (-x + 17) = y + y
12 + 17 = 2y
29 = 2y
y = 14.5
Then you can substitute y back into one of the original equations to solve for x:
14.5 = x + 12
x = 2.5
Therefore, the correct step is to add the equations to eliminate x.