Question

given the system below, read the table (step 1, step 2, and result), then answer whether the result is true or false. \

$$\begin{cases} 2x - 5y = -6 \\\\ x + 3y = 13 \\end{cases}$$

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$$\begin{tabular}{|c|c|} \\hline step 1 & multiply 1st equation by 3 and 2nd equation by -5. \\\\ \\hline step 2 & add the two new equations. \\\\ \\hline result & the ys are eliminated. \\\\ \\hline \\end{tabular}$$

choose the correct answer below. \bigcirc true \bigcirc false

Explanation:

Step1: Multiply equations as per Step 1

1st equation: \(2x - 5y = -6\), multiply by 3: \(3(2x - 5y)=3(-6)\) → \(6x - 15y = -18\)
2nd equation: \(x + 3y = 13\), multiply by -5: \(-5(x + 3y)=-5(13)\) → \(-5x - 15y = -65\)

Step2: Add the two new equations

Add \(6x - 15y = -18\) and \(-5x - 15y = -65\):
\((6x - 5x)+(-15y - 15y)=-18 - 65\) → \(x - 30y = -83\)

The \(y\)-terms are \(-15y\) and \(-15y\), which sum to \(-30y\), not eliminated. So the result "The \(y\)'s are eliminated" is false.

Answer:

False