Question

2x - 3y = 2\
5x + 9y = 27\
\
1 what can you multiply one equation by to be prepared to eliminate a variable?\
a multiply the top equation by 5\
b multiply the bottom equation by 3\
c multiply the top equation by 3\
d multiply the bottom equation by -5

Explanation:

To eliminate a variable (either \(x\) or \(y\)) in the system of equations \(

$$\begin{cases}2x - 3y = 2\\5x + 9y = 27\end{cases}$$

\), we look at the coefficients of \(y\). The coefficient of \(y\) in the top equation is \(-3\) and in the bottom equation is \(9\). If we multiply the top equation by \(3\), the coefficient of \(y\) becomes \(-9\), and when we add the two equations, the \(y\)-terms will be \(-9y + 9y = 0\) (eliminating \(y\)). Let's check the options:

• Option A: Multiplying the top equation by \(5\) gives \(10x - 15y = 10\). The \(x\)-coefficients would be \(10\) and \(5\), not helpful for elimination here.
• Option B: Multiplying the bottom equation by \(3\) gives \(15x + 27y = 81\). The \(y\)-coefficients are \(-3\) and \(27\), not opposites or same for easy elimination.
• Option C: Multiplying the top equation by \(3\) gives \(6x - 9y = 6\). Now, adding to the bottom equation \(5x + 9y = 27\) gives \(11x = 33\), eliminating \(y\). This works.
• Option D: Multiplying the bottom equation by \(-5\) gives \(-25x - 45y = -135\). Not helpful for elimination.

Answer:

C. Multiply the top equation by 3