Answered

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Using the graphing function on your calculator, find the solution to the system of equations shown below.

[tex]\[
\begin{array}{c}
3y + 3x = 2 \\
y + x = 8
\end{array}
\][/tex]

A. [tex]\( x = 3, y = 3 \)[/tex]

B. [tex]\( x = 1, y = 1 \)[/tex]

C. More than 1 solution

D. No solution

Sagot :

GinnyAnsweridn
Let's solve the given system of equations to determine if there are any solutions and, if so, what they are:

1. Rewrite the equations in slope-intercept form (i.e., [tex]\( y = mx + b \)[/tex]):

- For the first equation [tex]\( 3y + 3x = 2 \)[/tex]:
[tex]\[ 3y + 3x = 2 \implies 3y = 2 - 3x \implies y = \frac{2 - 3x}{3} \][/tex]

- For the second equation [tex]\( y + x = 8 \)[/tex]:
[tex]\[ y + x = 8 \implies y = 8 - x \][/tex]

2. Set the right-hand sides of the equations equal to each other to find the intersection point:

[tex]\[ \frac{2 - 3x}{3} = 8 - x \][/tex]

3. Clear the fraction by multiplying both sides by 3:

[tex]\[ 2 - 3x = 3(8 - x) \][/tex]
[tex]\[ 2 - 3x = 24 - 3x \][/tex]

4. Simplify the equation:

Notice that both sides have a [tex]\(-3x\)[/tex]:

[tex]\[ 2 - 3x + 3x = 24 - 3x + 3x \implies 2 = 24 \][/tex]

5. Analyze the resulting equation:

The simplified equation is [tex]\( 2 = 24 \)[/tex], which is a contradiction because 2 does not equal 24.

This contradiction means that there is no [tex]\(x\)[/tex] and [tex]\(y\)[/tex] pair that satisfies both equations simultaneously. Therefore, the system of equations represents parallel lines that do not intersect at any point.

Thus, the correct answer is:

D. No solution
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