Question

What is the solution of the following system using the substitution method? 3x + 2y = 11, x - 2 = -4y

1) The only solution is (12, -52)
2) The only solution is (4, -12)
3) There is no solution
4) There are an infinite number of solutions

Answer 1

To solve the system of equations using the substitution method, solve one equation for one variable and substitute that expression into the other equation. Then solve for the remaining variable. In this case, the system has no solution.

Step-by-step explanation:

To solve the system of equations using the substitution method, we need to solve one equation for one variable and substitute that expression into the other equation. Let's solve the second equation for x:

x - 2 = -4y

x = -4y + 2

Now substitute this expression for x into the first equation:

3(-4y + 2) + 2y = 11

-12y + 6 + 2y = 11

-10y + 6 = 11

-10y = 5

y = -0.5

Now substitute this value of y back into the second equation to find x:

x - 2 = -4(-0.5)

x - 2 = 2

x = 4

Therefore, the solution to the system of equations is (4, -0.5), which is not one of the given options.

The correct answer is option 3) There is no solution.