[August SAT] The BEST SAT Math Trick

What’s going on y’all 🤙

This SAT Math trick will show you how to solve sat questions quickly and score higher.

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☎️ 30 Minutes With John [Consultation]
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FAQ
Name: John
Where did you study - Emory University
What did you major in - Economics & Psychology
How long have you been teaching - Since 2012
Why do you decide to teach - It was tough for me to figure it all out when I was in high school, and my goal is to make it a lot easier for current students
Can you make videos on Reading & Writing - I don’t know those sections well enough to talk about them.
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[Wineblood]

y = -3x + 8 and y = 3x + 8, both straight and not parallel, so one intersection.

[aayudh.]

Okay but you need to know this. You can't have 2 solutions for linear equations. It's always either zero, one or infinitely many. If the equations are identical, they have infinitely many solutions. If, they have the same slope, they have zero solutions. and if its neither, they have one solutions. Always automatically eliminate option 'two'.

[wzpforall]

Identical equation = infinite solutions
Same slope = zero solutions
Different slope = one solution

[jaydenlin]

In the digital SAT, you have Desmos to use as you like. This is one of those questions that you simply plug into desmos and see if the lines are the same, parallel, or cross.

[loganxavier]

Two different lines that aren’t parallel will always only have one solution

[AgarioGameplays]

Y+3x=8
2y-6x=16

Y = 8-3x
So we replace
2(8-3x)-6x=16
Then 16-6x-6x=16
Which gives us
0=12x
So x=0/12 so x=0
Then we plug it in to the first equation y+3(0)=8
therefor Y=8 and X=0.
So there’s one solution

[greaterdanemark]

I really wish they’d word these questions in a more clear manner. It makes it so easy when someone just tells me what the question is *actually* asking

[liammoore]

y + 3x = 8
2y - 6x = 16

Easy trick:
Since 16 is a multiple of 8 by a factor of 2 just multiply the entire first equation by 2.
Set the new equation equal with the original second equation and you get

2y + 6x = 2y - 6x

Next subtract 2y from both sides.

Now 6x = -6x

So just by plugging in a few numbers you should see that zero is the only number that fits.

[guessWHOOO]

y+3x = 8
2y-6x = 16
Multiply first equation by 2 to get
2y+6x = 16, subtract both equations to get
12x = 0. Solve to get x = 0
Plug in 0 to y+3x=8, y=8.

[mr.maynard]

Thank you so much. You are my saving grace. I have been having so much trouble with this. Even though I've taken a SAT class nobody has giving me a short and easy way to do these types of questions.

[gabe_digg]

I was taught to label each equation A B C ... The just create algebra out of those which you solve. Helps alot when you get 'are they skew?' questions.

[armgrease]

Just use substitution by elimination.


Multiply the top equation by 2, cancel out the x'es, and the add the two equations together. You'd get 4y = 32, so y = 8. Plug that back into any equation and x would make the equation true, making it one solution.

This is standard teachings on ninth grade algebra 1 so anybody taking the Sat's should know it.

[HanzCastroyearsago]

If the equations are parallel (meaning they are shifted by a constance), the intersections will be 0. If the equations are identical, they share all solutions along the line, which is uncountable. If it intersects once it means the equations are neither of the above. These are the only possibilities, but if you’re running out of time just pick the 1 option.

[Tirelesswarrior]

Why does SAT give the "I quit" option?😅😅

[anon-a-moss]

Another thing to know is that you're working with two linear functions, which can only have 0 (parallel or same slope), 1 (for an intersection or different slopes) or infinite solutions (if both are the exact same function). Two solutions is impossible.

[CalculusIsFun]

Two straight lines which are not parallel can only intersect at a maximum of 1 point. It can be infinitely many or two, and the equations do not have same slope with a vertical phase shift (no solution) so it must be one solution.

Takes like 1 second.

[_ORONALDO]

This is something I learnt in 10th class

[ljltzoo]

You could just put both equations into the desmos calculator and see how many times they intersect, if they intersect once: one solution, if they dont intersect: no solution, if the lines are on top of each other (same line): then infinitely many solutions

[Roxve]

y+3x = 8 (1)

multiplying (1) by 2
2(y+3x) = 2y+6x = 2(8) = 16 (2)

2y - 6x = 16 (3)
adding (2) and (3)
2y + 6x + 2y - 6x = 16 + 16 = 32
4y = 32
y = 8

replacing y in (1)
y + 3x = 8
8 + 3x = 8
x = 0

thats how I would have wrote it in an exam, it's really easy to see in like 3 seconds

[ragavireddy]

We don't need to solve the equations to get the answer.
For ex:
The equations are in the form of
ax +by =c and a° x + b°y = c°.
So we just need to find the values of a/a°, b/b° and c/c°.
If
1) a/a°=b/b°=c/c° then the equations have infinite solutions as they are basically the same lines meaning they coincide at every point.
2) a/a° ≠ b/b° then the equations have one solution as they intersect at only one point.
3) a/a°=b/b° ≠c/c° then they have no solutions as they are parallel lines and never intersect each other.

So in this question,
a/a° = 1/2
b/b° = -1/2
c/c° = 1/2
As a/a° ≠ b/b°, the lines intersect at only one point thus they have only one solution.