Question
Solving Simultaneous Equations Using Substitution Quick Check
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)
Answers
GPT-4o mini
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**.
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**.