Final answer:
To solve the system of equations using elimination, multiply the first equation by 5 and the second by 7, subtract the results to eliminate x and solve for y. Substituting y=6 back into the original equations gives x=5. The solution is x=5 and y=6.
Step-by-step explanation:
To solve the system of equations given by 7x - 6y = -1 and 5x - 4y = 1 using elimination, we look to eliminate one of the variables by making the coefficients of either x or y the same in both equations. An effective approach would be to multiply the first equation by 5 and the second equation by 7, then subtract one from the other to remove the x variable.
After multiplying, we get:
Now we subtract the second from the first:
Which simplifies to:
Dividing both sides by -2 gives us:
To find x, we can substitute y = 6 back into one of the original equations, let's choose the second equation:
Therefore, the solution to the system of equations is x = 5 and y = 6.
Always remember to check the answer by substituting the values of x and y back into the original equations to see if they satisfy both equations.