Final answer:
Substitution is the more convenient method for solving the provided system of equations due to fractional coefficients that make elimination complex. The first equation can be easily manipulated to express x in terms of y, which can then be substituted into the second equation.Option A is the correct answer.
Step-by-step explanation:
To decide whether to solve the system of equations by substitution or elimination, we should look at the setup of the equations. The provided system of equations is:
- x/4 - 14y = 13
- -3x - 2y/3 = 7
In the case of the given system, the method of elimination might be more complicated due to fractional coefficients. Substitution, on the other hand, allows us to solve for one variable and then substitute that value into the other equation.
Since the first equation can be manipulated to express x in terms of y, which can then easily be substituted into the second equation, substitution could be the more convenient method here.
Let's solve the first equation for x:
- Multiply both sides by 4 to clear the fraction: x - 56y = 52
- Add 56y to both sides to isolate x: x = 56y + 52
We can take this expression for x and substitute it into the second equation. After substituting, you would just need to solve for y and then use the value of y to find x using the expression from the first equation.