You can put this solution on YOUR website! and
------------------------ we can solve this system by substitution or by addition
Let do it by substitution:
the first equation, we can solve in terms of ………move to the right
Now, substitute in second equation
…….move to the right
You can put this solution on YOUR website! Given the two equations:
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3x + y = 2
2x - y = 3
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This pair of equations is "nicely" arranged for solving by variable elimination because
one of the terms in the top equation [that term is +y] is equal but with the opposite
sign to the corresponding term in the bottom equation [that term is -y]. If you add these
two equations vertically, the y-column will disappear because +y added to -y cancels
out.
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In the x column the 3x adds to the 2x and equals 5x. As we mentioned, in the y column the
+y and the -y sum to zero and therefore are gone. And on the other side of the equal sign
the +2 and the +3 add to 5. So, after adding the two equations vertically you are left
with 5x = 5. You can solve this equation for x by dividing both sides of this equation by
5 (the multiplier of the x) and you get:
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x = 5/5 = 1
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So you now know that x = 1
.
You can then go back to either one of the two equations you were given and replace x by 1
in that equation and then solve for y. Let's go back to the first equation:
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3x + y = 2
.
replace x by 1 and the equation becomes:
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3(1) + y = 2
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do the multiplication of 3 times 1 and the equation reduces to:
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3 + y = 2
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Get rid of the 3 on the left side by subtracting 3 from both sides of the equation to
reach the solution:
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y = 2 - 3 = -1
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So the solution to this problem is x = 1 and y = -1
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Hope this helps you to understand the problem a little better.
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