Final answer:
To solve the system of equations using elimination, multiply one of the equations by a number that will make the coefficients of one variable opposite in the two equations. Then add the resulting equations to eliminate the variable. Finally, solve for the remaining variable.
Step-by-step explanation:
To solve the system of equations using elimination, we'll multiply the second equation by -2 to make the coefficients of x in both equations equal. This will allow us to eliminate x when we add the equations together. So, the new system of equations becomes:
5x + 10y = 7
-8x - 16y = -6
Adding the equations together, we get:
-3y = 1
Dividing both sides by -3, we find that y = -1/3. Substituting this value back into one of the original equations, we can solve for x:
5x + 10(-1/3) = 7
Simplifying, we find that 5x - 10/3 = 7
Adding 10/3 to both sides, we have 5x = 31/3
Dividing both sides by 5, we find that x = 31/15
Therefore, the solution to the system of equations is x = 31/15 and y = -1/3.