Final answer:
To solve the system of equations 4x-3y=47 and 5x+4y=-11 using elimination by addition, we can multiply the equations by appropriate numbers to make the coefficients of the y terms the same. After adding the equations, the y terms cancel out, leaving us with an equation to solve for x. Substituting the value of x into one of the original equations gives us the solution for y. The solution to the system of equations is x=5 and y=-9.
Step-by-step explanation:
To solve the system of equations 4x-3y=47 and 5x+4y=-11, we can use the method of elimination by addition.
We can multiply the first equation by 4 and the second equation by 3 to make the coefficients of the y terms the same.
So, the equations become 16x-12y=188 and 15x+12y=-33. When we add these two equations together, the y terms cancel out, and we are left with 31x=155. Dividing both sides by 31, we find that x=5.
Substituting this value of x into one of the original equations, we can solve for y. Let's use the first equation: 4(5)-3y=47. Simplifying this equation, we get -3y=27. Dividing both sides by -3, we find that y=-9.
Therefore, the solution to the system of equations is x=5 and y=-9.