Solving Linear Equations with No or Infinite Solutions

In this video, we look at solving linear equations with no solution, or an infinite number of solutions. When an equation has no solution is called a contradiction. When an equation has an infinite number of solutions, it is called an identity.

[jasonsaysno]

okay, so this only works with problems with the distributive property and with problems where both sides have equal variable amounts?

[chrisg]

-2 = 2 - 6(n - n), -2 = 2 - 6(n - n), -2 = 2. With you so far, but what if we decide the solution is worth checking out? Plug in 2 for -2 in the original equation, and we get 2 = 2 - 6(n - n), yielding 2 = 2. True, but not a useful solution either. What about 2(2 +6n) = 3 + 4(2 + 3n), 4 + 12n = 3 + 8 + 12n,   4+12n = 3 + 8 + 12n, 4 = 11. Don't despair, take it as a sign to plug in 11 for 4 in the original equation. 2(2 + 6n) = 3 + 11(2 + 3n), so now 4 + 12n = 3 + 22 + 33n, 12n - 33n,   3 + 22 - 4, -21n = 21, n = -1. Hooray.

[serenanguyen]

wait so if my equation is x-2 = -(x-2) would that be no solution?

[suprith]

My problem is

How many solutions does the system have?
x+3y=0
12y=-4

This is infinite solutions right?

[lixpixies]

How do you solve each system of linear equation graphically?

[zwrtsfatima]

What would be the answer for -5 + 4 (× - 7) = -27 + 2x