MYP Standard Mathematics Systems of Linear Equations Questionbank

To solve $3x + y = 10$ and $x - 2y = 1$ by substitution, one could isolate $y$ in the first equation to get $y = 10 - 3x$. Substituting this into the second equation results in which simplified one-variable equation?

Fill in the blank: To eliminate the variable $y$ from the system below by addition, one could multiply the first equation by 2 and the second equation by ____.

True or False: The equations $x - y = 4$ and $2y - 2x = -8$ represent coincident lines.

Given a system in the form:

If the ratios of the coefficients satisfy $\frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \frac{c_1}{c_2}$, what is the geometric relationship between the two lines?