I can't remember how to graph this to answer the question. what is the solution of the system of equations?
Consistent or inconsistent?
Dependent or independent?
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The equations are saying the same thing. Note that if you multiply either equation by -1 you will get the other. Therefore they are consistent, but they are also dependent. Every point on that line is a solution.
Is it a rule to multiply by 1 to get the solution for problems like these?
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The equation has infinitely many solutions yes. The way to get solutions is typically to add multiples of the equations to eliminate one variable then solve for the other variable.
2x+3y = 5 (eq1)
4x + y = 2 (eq2)
We see that
\[-2*(eq1) \implies -2(2x+3y) = -2(5)\implies -4x -6y = -10\]
4x +y = 2 (eq2)
+ -4x-6y = -10 -2(eq1)
-5y = -8 \(\implies y=8/5\)
Then we plug back in to find x
\[4x+y = 2 \implies 4x + 8/5 = 2 \implies 20x + 8 = 10\]
\[\implies 20x = 2 \implies x = 1/10\]