Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To solve the system of equations given by [tex]\( y = 4x - 8 \)[/tex] and [tex]\( y = 4x + 2 \)[/tex], we need to determine if there is a point [tex]\((x, y)\)[/tex] that satisfies both equations simultaneously.
1. Set the equations equal to each other:
Since both equations are equal to [tex]\( y \)[/tex], we can set them equal to each other:
[tex]\[ 4x - 8 = 4x + 2 \][/tex]
2. Simplify the equation:
To find the value of [tex]\( x \)[/tex], we aim to isolate [tex]\( x \)[/tex]. Let's subtract [tex]\( 4x \)[/tex] from both sides of the equation:
[tex]\[ 4x - 4x - 8 = 4x - 4x + 2 \][/tex]
Simplifying both sides, we get:
[tex]\[ -8 = 2 \][/tex]
3. Analyze the result:
The equation [tex]\( -8 = 2 \)[/tex] is a contradiction, meaning it is not true. This indicates that there is no value of [tex]\( x \)[/tex] that will satisfy both equations simultaneously.
Since the simplified result led to a contradiction, there is no solution where both equations intersect.
Therefore, the correct answer is:
[tex]\[ \boxed{\text{None of the above}} \][/tex]
1. Set the equations equal to each other:
Since both equations are equal to [tex]\( y \)[/tex], we can set them equal to each other:
[tex]\[ 4x - 8 = 4x + 2 \][/tex]
2. Simplify the equation:
To find the value of [tex]\( x \)[/tex], we aim to isolate [tex]\( x \)[/tex]. Let's subtract [tex]\( 4x \)[/tex] from both sides of the equation:
[tex]\[ 4x - 4x - 8 = 4x - 4x + 2 \][/tex]
Simplifying both sides, we get:
[tex]\[ -8 = 2 \][/tex]
3. Analyze the result:
The equation [tex]\( -8 = 2 \)[/tex] is a contradiction, meaning it is not true. This indicates that there is no value of [tex]\( x \)[/tex] that will satisfy both equations simultaneously.
Since the simplified result led to a contradiction, there is no solution where both equations intersect.
Therefore, the correct answer is:
[tex]\[ \boxed{\text{None of the above}} \][/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.