Slide until the lines are parallel
Leave the constants in, add sliders, and watch for parallel.
2:25 · Systems of 2 Linear Equations in 2 Variables
Worked in this video
a(2x + y) − 3y = 5x − 7 and 9x + 3y = c
The system has infinitely many solutions. What is the value of a + c?
Type the first equation exactly as it is printed — no expanding, no collecting — and leave a and c in as sliders. Infinitely many solutions means one line, not two, so build one line. Dragging a turns the first line, and at a = 4 the two are parallel. Dragging c slides the second line without turning it, and at c = −21 they become a single line. On paper you would distribute the a, move the x terms across, collect the y terms, and only then match coefficients in a ratio.
Answer: a + c = −17