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### Course: Class 10 (Old)>Unit 3

Lesson 3: Number of solutions algebraically

# Forming systems of equations with different numbers of solutions

Sal write an equation that along with the equation 4x + 5y = 2 forms a system of equations with infinitely many solutions. Created by Sal Khan.

## Want to join the conversation?

• when 0;10 says 'infinitely many solutions'' does it mean the solutions go on forever? Because in doing the problems their is only one way to do them.
• The solution to a system of equations is the point or points at which their graphs intersect. Thus, when you have two ways of expressing the same equation, you get infinitely many intersections (because they are identical). So, every point that lies on the graph of one equation (and there are infinitely many such points) will also lie on the graph of the other.
• Can you have systems of equations with something other than lines?
• Yes. These are called non-linear systems, and when solving them, you are finding the points where other types of graphs intersect each other. These systems can have more than one solution (yet without having an infinite number of solutions as is the case with lines).

For example, imagine the graph of two parabolas -- one pointing up and the other down. You can position these in a way where there are two points of intersection. To find those, you would solve a non-linear system.
• I am having trouble determining how to complete some of the problems in "understanding solution methods to systems of equations" the video linked doesnt really cover this module clearly. In some of the questions it asks you to "add" the equations together, but in the hints it does the problem sometimes by "subtracting" when it tells you to "add", then in other problems it tells you to "add" them together and it does the problem by "adding" them - I dont understand this discrepancy. Thx in advance for any help!
• When using elimination to solve a system of equations, adding OR subtracting the equations together are valid processes. When do you add and when do you subtract?
If the coefficients of the variable you are eliminating are exactly the same, then subtract.
Example...
3x + 5y = 12
3x + 4y = 6
Subtract the equations to get y = 18

If the If the coefficients of the variable you are eliminating are exactly the same but with different signs, then add.
Example
3x + 7y = 15
-3x - 6y = 6
Add the equations together to get y = 21
• I don't get anything on "graphically understanding solution methods to systems of equation". Can you explain it.
• I don't get any right either! The questions don't relate, and the hints don't make sense!
• HELP! I am stuck on a problem called:
Graphically understanding solution methods to systems of equations.
This is the last question I have to finish before the end of the summer. I have watched all the videos and understand everything except for adding and subtracting the equations. I have tried for five or six days and I can't get it right, I look through the hints and study it all but I cant get it right! No one I have asked in my house can help and I am frustrated. Please help.
-Chance.
• I am too confused in this topic in the last question of the video
• At whats the porpose of multipying by 2?