Question

Which method is better to solve the following system of equations?

x = 3y + 6
4x + y = 18
(A) Substitution method
(B) Elimination method
(C) Both methods are equally good.
(D) Neither method is good.

Answer 1

The substitution method is more suitable for the system of equations provided since one equation is already solved for x, allowing for straightforward substitution and solving.

Step-by-step explanation:

To determine which method is better for solving the system of equations:

• x = 3y + 6
• 4x + y = 18

The substitution method is an appropriate choice here since one equation is already solved for x. We can substitute the expression for x from the first equation into the second equation and solve for y. After finding y, we can substitute y back into the first equation to find x.

Step-by-step using substitution:

1. Substitute x from the first equation into the second: 4(3y + 6) + y = 18.
2. Simplify and solve for y: 12y + 24 + y = 18.
3. Find y: 13y = -6, y = -6/13.
4. Substitute y back into the first equation to find x: x = 3(-6/13) + 6.
5. Solve for x: x = -18/13 + 78/13, x = 60/13.

Thus, the solution to the system is x = 60/13 and y = -6/13. Answer choice (A) Substitution method is better for solving the given system of equations.