Final answer:
To solve the system of equations using the elimination method, add the equations vertically to eliminate the y variable. Then, solve for x by dividing both sides by 9. Substitute the value of x back into one of the original equations to solve for y.
Step-by-step explanation:
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. In this case, we can eliminate the y variable by adding the equations vertically:
7x - y = 40
+ (add the two equations vertically)
3x + y = 30
9x = 70
Divide both sides by 9:
x = 70/9
Now substitute the value of x into one of the original equations to find the value of y:
7x - y = 40
7(70/9) - y = 40
70 - y = 360/9
70 - y = 40
-y = 40 - 70
-y = -30
y = 30
Therefore, the solution to the system of equations is x = 70/9 and y = 30.