Solving Simultaneous Equations Using Substitution Quick Check

Question

1 of 51 of 5 Items
Question
Use the substitution method to solve the system 2x+3y=4, −4x−6y=−8.(1 point)
Responses

(−1,2)
left parenthesis negative 1 comma 2 right parenthesis

infinite solutions
infinite solutions

no solution
no solution

(2−1)

Answer 1

To solve the system of equations using the substitution method, we have the following equations:

1. \(2x + 3y = 4\) (Equation 1)
2. \(-4x - 6y = -8\) (Equation 2)

First, notice that Equation 2 can be simplified.

Step 1: Simplify the second equation

Dividing Equation 2 by -2 gives:

\[ 2x + 3y = 4 \]

Now we see that both equations are essentially the same, meaning that they represent the same line.

Step 2: Determine the type of solution

Since both equations are identical, they have infinite solutions. Any point (x, y) that satisfies \(2x + 3y = 4\) will also satisfy \(-4x - 6y = -8\).

Conclusion

The correct answer is infinite solutions.