To eliminate one of the variables by adding the equations, we need to make the coefficients of one of the variables (either \(x\) or \(y\)) the same or opposites in both equations.
Let's look at the given system:
- \(-6x + 4y = 26\) (Equation 1)
- \(5x + 2y = 37\) (Equation 2)
We can focus on eliminating \(y\). The coefficient of \(y\) in Equation 1 is 4, and in Equation 2 it is 2. To make them the same, we can multiply Equation 2 by 2. This will change the coefficient of \(y\) in Equation 2 to 4, making it possible to eliminate \(y\) when we add the equations.
Let's analyze the options:
a. Multiply the first equation by 2 b. Multiply the second equation by 2 c. Multiply the second equation by -2 d. Multiply the first equation by -2
The correct choice to eliminate \(y\) is: b. Multiply the second equation by 2.
After performing this operation, the modified system will be:
- \(-6x + 4y = 26\)
- \(10x + 4y = 74\)
Now, when we add these equations, the \(y\) terms will cancel out:
\[ (-6x + 4y) + (10x + 4y) = 26 + 74 \]
This will lead us to a simpler equation that we can solve for \(x\).