Question

9x - 7y = -3\
-3x + 5y = 9\
how can you eliminate the x-terms in this system?\
\
$9x - 7y = -3$\
$-3x + 5y = 9$ \\u2190 multiply by? on both sides.\
0\
1\
2\
3

Explanation:

Step1: Analyze x - coefficients

The x - coefficient in the first equation is \(9\), and in the second equation is \(- 3\). We want to make the coefficients of \(x\) in both equations such that they are additive inverses (or equal) so that we can eliminate \(x\) by adding (or subtracting) the equations.
Let the multiplier for the second equation be \(k\). We want \(k\times(-3)=-9\) (so that when we add the two equations, the \(x\) terms will be \(9x+(-9x) = 0\)). Solving \(k\times(-3)=-9\) for \(k\), we divide both sides by \(-3\): \(k=\frac{-9}{-3}=3\).

Step2: Verify

If we multiply the second equation \(-3x + 5y=9\) by \(3\), we get \(3\times(-3x)+3\times(5y)=3\times9\), which simplifies to \(-9x + 15y = 27\). Now, if we add this new equation to the first equation \(9x-7y=-3\), the \(x\) - terms will be \(9x+(-9x)=0\), and we have eliminated the \(x\) - terms.

Answer:

3