Answered

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Laura graphs these equations and finds that the lines intersect at a single point, [tex]$(1.5, -1.5)$[/tex].

[tex]\[
\begin{aligned}
\text{Equation A:} & \quad -2y + 6x = 12 \\
\text{Equation B:} & \quad 4x + 12y = -12
\end{aligned}
\][/tex]

Which statement is true about the values [tex]\( x = 1.5 \)[/tex] and [tex]\( y = -1.5 \)[/tex]?

Sagot :

GinnyAnswer
To determine whether the values [tex]\( x = 1.5 \)[/tex] and [tex]\( y = -1.5 \)[/tex] satisfy each of the given equations, we should substitute these values into both equations and check if the resulting expressions are true.

Let's start with the first equation, Equation A:
[tex]\[ -2y + 6x = 12 \][/tex]

1. Substitute [tex]\( x = 1.5 \)[/tex] and [tex]\( y = -1.5 \)[/tex] into Equation A:
[tex]\[ -2(-1.5) + 6(1.5) = 12 \][/tex]

2. Simplify the equation:
[tex]\[ -2 \times (-1.5) + 6 \times 1.5 \][/tex]
[tex]\[ 3 + 9 = 12 \][/tex]

3. Check the result:
[tex]\[ 12 = 12 \][/tex]
This statement is true.

Now, let's check the second equation, Equation B:
[tex]\[ 4x + 12y = -12 \][/tex]

1. Substitute [tex]\( x = 1.5 \)[/tex] and [tex]\( y = -1.5 \)[/tex] into Equation B:
[tex]\[ 4(1.5) + 12(-1.5) = -12 \][/tex]

2. Simplify the equation:
[tex]\[ 4 \times 1.5 + 12 \times (-1.5) \][/tex]
[tex]\[ 6 - 18 = -12 \][/tex]

3. Check the result:
[tex]\[ -12 = -12 \][/tex]
This statement is also true.

Therefore, the values [tex]\( x = 1.5 \)[/tex] and [tex]\( y = -1.5 \)[/tex] satisfy both equations:

1. For Equation A: [tex]\[ -2y + 6x = 12 \][/tex]
[tex]\[ -2(-1.5) + 6(1.5) = 12 \][/tex]
is true.

2. For Equation B: [tex]\[ 4x + 12y = -12 \][/tex]
[tex]\[ 4(1.5) + 12(-1.5) = -12 \][/tex]
is true.

Hence, the statement that is true about the values [tex]\( x = 1.5 \)[/tex] and [tex]\( y = -1.5 \)[/tex] is that they satisfy both of the given equations.
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