Answered

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.



Answer :

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.