Final answer:
To solve the system of equations using elimination, we multiply the equations to eliminate a variable, subtract the equations to eliminate the other variable, and solve for the remaining variable. In this case, we find that x=-20.2 and y=13.
Step-by-step explanation:
To solve the system of equations using elimination, we need to eliminate one variable by multiplying one or both equations by suitable constants so that the coefficients of one of the variables are the same. In this case, we'll multiply the first equation by 6 and the second equation by 5 to eliminate the y variable.
Multiplying the first equation, we get 30x + 42y = -60. Multiplying the second equation, we get 30x + 25y = 170. Now, subtract the two equations to eliminate the x variable.
Subtracting the equations, we get 17y = 230. Divide both sides by 17 to solve for y, giving us y = 13. Substituting this value back into the first equation, we can solve for x. Plugging in y = 13, we get 5x + 7(13) = -10. Simplifying, we find 5x + 91 = -10. Subtracting 91 from both sides, we find 5x = -101. Dividing both sides by 5, we get x = -20.2.