Let h and c be the cost of the hamburger and chicken, respectively. Then, the first statement "5 hamburger and 5 chicken for a total of $40" can be written as
and the second statement "4 hamburger and 7 chicken for $44" can be written as
Then, we have the following system of equaitons:
Solving by elimination method.
By multiplying the frist equation by -4 and the second one by 5, we have an equivalent system of equations:
So, the variable h has opposite coefficients then by adding both equations we can eliminate variable h, that is,
Then, c is given by
Finally, we can find h by substituting this result into one of the 2 equations of our system. If we choose equation 1, we get
which gives
Therefore, the cost of the hamburger is $4 and the cost of the chicken is $4 too