Final answer:
To solve the system of equations -7x - 4y = -44 and 7x - 3y = 16, we can use the method of elimination. The solution is x = 14/5 and y = 6/5.
Step-by-step explanation:
To solve the system of equations -7x - 4y = -44 and 7x - 3y = 16, we can use the method of elimination.
Step 1: Multiply the second equation by 2 to make the coefficients of x in both equations cancel each other out:
-7x - 4y = -44
14x - 6y = 32
Step 2: Add the two equations together to eliminate x:
-7x + 14x - 4y - 6y = -44 + 32
Step 3: Simplify and solve for y:
7x - 10y = -12
-10y = -12
y = -12 / -10
y = 6/5
Step 4: Substitute the value of y back into one of the original equations and solve for x:
7x - 3(6/5) = 16
7x - 18/5 = 16
7x = 16 + 18/5
7x = 80/5 + 18/5
7x = 98/5
x = 98/5 ÷ 7
x = 14/5
Therefore, the solution to the system of equations is x = 14/5 and y = 6/5.