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# Number of solutions to a system of equations

Sal is given three lines on the coordinate plane, and identifies one system of two lines that has a single solution, and one system that has no solution. Created by Sal Khan and Monterey Institute for Technology and Education.

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• Could someone help me understand how to solve a equation then graph it if the equation is in standard form?
• Take it out of standard form and put it in y intercept form then find your cordinate point and graph them that should help you
• Is there any difference between a coordinate plane and a coordinate grid?
• Not really
(1 vote)
• How do you figure out if the problem has infinite, one, or no solutions?
• (I'm going to reference parallel lines multiple times) Assuming you're talking about straight line equations (y=mx+b), if the equations have the same slope, they are either going to have no solutions, or infinite solutions. To picture this, if they have the same slope, but different y-int. they would be parallel lines, which never touch, which is why it has no solutions. Or, if they have the same slope, and same y-int, it would be the same line on top of itself, so every point on one of the lines shows up on the other line, which is why it has infinite solutions. If they have different slopes, then it will only have one solution, opposite from parallel lines, these will intersect once, and only once, which it why it will only have one solution. Sorry if this is too wordy, but hope this helps
• so....correct me if i am wrong...but it seems like the system of two lines that has no solution has the same slope and has different y intercept
• That is correct - that also means that the lines are parallel
• How can I tell if I graphed it right
• there really are no sure signs that you have graphed "right"; just make sure that your incriments are small and equal. If you have graphed right, then the point of intersection that you get should be the coordinate (x,y) points that satisfy your system of equations. hope that helps!
• If I were given a series of equations, say,
2x+2y+4z = 6
3x+6y-5z = 11
Ax+7y-2z = 3 and then asked to give a value of A for which the equations are consistant, how would I go about that? I got this question (not the same equations but the same format) in an assignment (not one that I'm getting any NCEA credits for) and I'm a little lost. I was just wondering if anyone could give me some tips, or point me towards a video that addresses this kind of problem.
• what is the difference between solving systems graphically and solving algebraically
• It's just as it sounds, solving systems graphically involves utilizing the coordinate plane to visualize the problem, while if you solve it algebraically you're only using the given algebraic equations and the methods of algebra.
• When it says to use standard form, do you reach standard form by algebraically transferring numbers until y is on the left, and x and whatever other numbers there may be are on the right?