Final answer:
To solve the system of equations, multiply the second equation by 3 and the first equation by 4 to make the coefficients of x equal. Add the two equations together and solve for y. Substitute the value of y into one of the original equations and solve for x. The solution is (4,1).
Step-by-step explanation:
To solve the system of equations:
3x + 4y = 16
-4x - 3y = -19
We can use the method of substitution or elimination. Let's use the elimination method:
Multiply the second equation by 3 and the first equation by 4 to make the coefficients of x in both equations equal:
12x + 16y = 64
-12x - 9y = -57
Add the two equations together:
7y = 7
Divide both sides by 7:
y = 1
Substitute this value of y into one of the original equations (let's use the first equation):
3x + 4(1) = 16
3x + 4 = 16
Subtract 4 from both sides:
3x = 12
Divide both sides by 3:
x = 4
Therefore, the solution to the system of equations is (4,1).