Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Ian graphs these equations and finds that the lines intersect at a single point, [tex](-2,-0.5)[/tex].

[tex]\[
\begin{array}{|l|c|}
\hline
\text{Equation A:} & 4y - 3x = 4 \\
\text{Equation B:} & -2x - 8y = 8 \\
\hline
\end{array}
\][/tex]

Which statement is true about the values [tex]x = -2[/tex] and [tex]y = -0.5[/tex]?

A. They satisfy equation B but not equation A.
B. They are the only values that make both equations true.
C. They show that the equations represent the same line.
D. They satisfy equation A but not equation B.

Sagot :

GinnyAnswer
To determine which statement is true about the values [tex]\( x = -2 \)[/tex] and [tex]\( y = -0.5 \)[/tex], we need to check if these values satisfy the given equations.

The equations provided are:

1. Equation A: [tex]\( 4y - 3x = 4 \)[/tex]
2. Equation B: [tex]\( -2x - 8y = 8 \)[/tex]

Let's verify if the point [tex]\((-2, -0.5)\)[/tex] satisfies each equation.

### Step-by-Step Verification

#### Check Equation A:

Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = -0.5 \)[/tex] into [tex]\( 4y - 3x = 4 \)[/tex]:

[tex]\[ 4(-0.5) - 3(-2) = 4 \][/tex]
[tex]\[ -2 + 6 = 4 \][/tex]
[tex]\[ 4 = 4 \][/tex]

This statement is true, so the point [tex]\((-2, -0.5)\)[/tex] satisfies Equation A.

#### Check Equation B:

Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = -0.5 \)[/tex] into [tex]\( -2x - 8y = 8 \)[/tex]:

[tex]\[ -2(-2) - 8(-0.5) = 8 \][/tex]
[tex]\[ 4 + 4 = 8 \][/tex]
[tex]\[ 8 = 8 \][/tex]

This statement is also true, so the point [tex]\((-2, -0.5)\)[/tex] satisfies Equation B as well.

Since [tex]\((-2, -0.5)\)[/tex] satisfies both equations, the correct statement would be:

B. They are the only values that make both equations true.

Therefore, the appropriate conclusion is:
[tex]\[ (x = -2, y = -0.5) \][/tex] are the values that satisfy both equations [tex]\( 4y - 3x = 4 \)[/tex] and [tex]\( -2x - 8y = 8 \)[/tex], making Statement B the correct answer.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.