SAT Math Hack7 Substitution vs Elimination

Indiziert: 2026-05-16

[00:00:00]Systems of equations.

[00:00:02]They show up on almost every SAT and most students waste time on them. Not because they can't solve them, but because they pick the wrong method.

[00:00:10]Today, I'm giving you a simple hack.

[00:00:12]One quick look at the problem and you'll know exactly which method is faster.

[00:00:17]Substitution or elimination.

[00:00:19]By the end of this video, you'll have a decision framework that saves you 30 to 60 seconds per problem.

[00:00:24]Let's get into it.

[00:00:27]Here's the thing.

[00:00:29]Most students pick randomly. They see a system and just start doing whatever feels right.

[00:00:34]Don't do that. There are only two questions you need to ask yourself.

[00:00:38]Number one, is a variable already isolated? If yes, substitution.

[00:00:42]Number two, do the coefficients line up nicely? If yes, elimination.

[00:00:47]That's it. Two checks, two seconds, and you've just saved yourself a ton of work.

[00:00:52]Let me show you exactly what I mean.

[00:00:55]If a variable is already isolated like y = 3x - 2, you substitution.

[00:01:00]Look at this system. The first equation already tells you what y is.

[00:01:04]So, you take that expression and you plug it right into the second equation.

[00:01:08]2x + 3x - 2 = 8. Combine like terms.

[00:01:12]5x = 10, x = 2.

[00:01:15]Then plug back in to get y = 4.

[00:01:17]Done.

[00:01:18]The signal is simple. If you see y = something or x = something, go straight to substitution.

[00:01:25]It also works when a variable has a coefficient of 1 or -1 because isolating it takes one easy step.

[00:01:33]Now, if the coefficients line up nicely, elimination is your move.

[00:01:37]Look at this system.

[00:01:38]3x + 2y = 10.

[00:01:40]3x - y = 1.

[00:01:43]See how both equations have 3x? That's your signal.

[00:01:46]Subtract one equation from the other and the x terms cancel out completely.

[00:01:50]You're left with 3y = 9.

[00:01:53]y = 3.

[00:01:54]Plug back in and x = 4/3.

[00:01:57]Here's what to look for. Same coefficients, subtract to cancel.

[00:02:01]Opposite coefficients like 2y and -2y add to cancel.

[00:02:05]And if the coefficients are close, just multiply one equation by a small number to match them up. Elimination keeps things clean.

[00:02:14]All right, your turn.

[00:02:15]Look at this system. x = 5y + 1 and 3x - 4y = 14.

[00:02:21]Before I solve it, pause the video and decide substitution or elimination.

[00:02:26]Okay, what do you notice about that first equation? x is already isolated.

[00:02:30]That's a dead giveaway.

[00:02:32]Substitution.

[00:02:33]Plug 5y + 1 in for x.

[00:02:36]You get 3 * 5y + 1 - 4y = 14.

[00:02:39]That's 15y + 3 - 4y = 14. 11 = 11, y = 1.

[00:02:45]And x = 6.

[00:02:47]The decision took 2 seconds.

[00:02:49]But it saved you over 30 seconds of messy algebra. That's the hack.

[00:02:54]Here's your cheat sheet. Screenshot this. Save it. Memorize it before test day.

[00:02:59]If you see y equals something or x equals something, substitution.

[00:03:03]Plug it right in.

[00:03:04]If you see the same coefficient on a variable in both equations, elimination.

[00:03:09]Subtract to cancel.

[00:03:10]If the coefficients are opposites like 2y and -2y, add to cancel.

[00:03:15]If a variable has a coefficient of 1 or -1, substitution because isolating it is easy.

[00:03:22]And if everything looks messy with fractions, elimination. Multiply to clear the fractions, then cancel. Pro tip, when both methods seem equally good, go with elimination. Fewer steps, fewer sign errors.

[00:03:35]That's the whole hack.

[00:03:37]Choose the method that reduces steps.

[00:03:39]Don't just dive in.

[00:03:40]Take 5 seconds to scan the problem first.

[00:03:43]Variable isolated, substitution.

[00:03:45]Coefficients match, elimination.

[00:03:48]This one habit can save you 3 to 5 minutes across a full SAT math section.

[00:03:53]And on a time test, those minutes are everything. Practice this with 10 systems tonight.

[00:03:58]Before you solve each one, write down which method you're choosing and why.

[00:04:02]Train that instinct now, and on test day it'll be automatic.

[00:04:06]If this helped, drop a like and subscribe for more SAT math hacks. Visit www.satprep1600.com for more.

[00:04:14]See you in the next one.