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### Course: Algebra basics>Unit 4

Lesson 2: Solutions to two-variable linear equations

# Completing solutions to 2-variable equations

Given a 2-variable equation and the x or y values of a solution, Sal finds the value of the other variable in the solution.

## Want to join the conversation?

• In the first question, when x = -5 and you have to find the value of Y, how come he decided to subtract 2y on either side? And why in the next one did he add 3x?
• You could have done it either way (subtract 2y or subtract 7y/ add 3x or subtract 5x) but by moving the smallest number (2y and -3x), you will keep the coefficient of the variable positive so that you do not have to divide by a negative number.
• this stuff does not make sents to me i only understand regual math
• It's not that hard once you get the hang of it-- keep trying! You can do it!
• So, if these are linear equations, what would be an example of a non-linear equation?

Would non-linear equations be calculus?
• No, the two functions that are not linear in Algebra I are Quadratic equations which form parabolas and Exponential equations which will approach a horizontal asymptote and increase quickly as you move either to the right (for a exponential growth and to the left for an exponential decay. You will learn other equations such as absolute value, cubic, square root, etc. before you reach calculus.
• If y=-8 when x=-5 then shouldn't x automatically be 5 when y=8?
• No, you can't automatically assume something like that. The reason both (-5,-8) and (5,8) are solutions to this equation is because they show up on the equation's line. Sal later says the (simplified) equation for the question is y=8x/5. To make this answer more clear, another equation, such as y=x-3, when x=-5, y is equal to -8, but when x equals 5, y equals 2. Hope this helps
• At . why is the subtraction of a negative still equal -40? Isn't it a negative minus a negative makes the negative positive for the second number or am I wrong?
• If the problem was: `- ( - 40)`, then you are correct. It becomes `+40`
But, the problem in the video is: `- 15 - 25`.
Visualize this on a number line, or draw a number line.
You got to -15, then you need to take away 25. This moves you further left on the number line and you end up on -40.

Hope this helps.
• how do you solve a question like this 4x+-6+10
• Since this is an expression, the only thing you can do is simplify. If it were 4x + (-6) + 10 = 24, you would add like terms, which are -6 and 10. Your equation would become 4x + 4 = 24. Subtract 4 from both sides, becoming 4x = 20. Now, divide both sides by 4, and you get x = 5. Your answer is 5.
Hope this helps.
• At How did he do that i really don't get the asnwer or the plot of this problem? I'm just confused.
• The trick is to keep the y-values balanced on both sides of the equation seeing as there are two of those but khan academy got a whole other unit dedicated solely to this topic; Solving equations & inequalities under Algebra 1. You should understand this better if you got a strong foundation there.
• when the equation was simplified to 5y=8x why did it become y= 8/5x?
• Because 5y was divided from both sides, and 8/5 just means 8 divided by 5
• i got the question to find x (y was -2) in the equation y+2=−3(x−4), and one of the steps is to go from 0=-3(x-4) to 0=x-4. can anyone tell me where the -3 went?