A: 6x − 3y = −4
B: −4x − y = 5
To solve this system of equations by elimination, what could you multiply each equation by to cancel out the x-variable?
To solve this system of equations by elimination, we need to multiply each equation by a certain factor so that the coefficients of the x-variable in both equations become additive inverses (i.e., add up to zero), allowing us to eliminate the x-variable when we add the equations together.
Let's consider equation A: 6x − 3y = −4.
To cancel out the x-variable, we need to multiply equation A by a factor such that the coefficient of x becomes the additive inverse of the coefficient of x in equation B. The coefficient of x in equation B is -4.
The additive inverse of -4 is 4. Therefore, to cancel out the x-variable, we can multiply equation A by 4.
By multiplying equation A by 4, we get:
4 * (6x - 3y) = 4 * (-4)
Simplifying this equation gives us:
24x - 12y = -16
Now, equation A has been multiplied by 4, and the x-variable will cancel out when we add it to equation B.
multiply the bottom equation by 6
multiply the top equation by 4