Final answer:
To solve the system of equations -x + 4y = 16 and 3x - y = 7, you can use the method of elimination. Multiply the second equation by 4 to make the coefficients of y the same, then add it to the first equation to eliminate y. Solve for x and substitute back into one of the original equations to find y. The solution is x = 4 and y = 5.
Step-by-step explanation:
To solve the system of equations -x + 4y = 16 and 3x - y = 7, we can use the method of substitution or elimination. Let's use the method of elimination. Start by multiplying the second equation by 4 to make the coefficients of y the same. This gives us 12x - 4y = 28. Now, add this equation to the first equation to eliminate y: -x + 4y + 12x - 4y = 16 + 28. Simplifying this, we get 11x = 44. Divide both sides by 11 to solve for x: x = 4.
Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. Let's use the first equation: -4 + 4y = 16. Add 4 to both sides: 4y = 20. Divide both sides by 4 to solve for y: y = 5.
Therefore, the solution to the system of equations is x = 4 and y = 5.