Solve the system of equations 3x-2y=7 and 4x+2y=14?
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We notice that we can solve the system using elimination method. All we have to do is to add the 1st equation to the 2nd one and we'll get:
3x - 2y + 4x + 2y = 7 + 14
We'll eliminate y and we'll get:
7x = 21
We'll divide both sides by 7:
x = 3
Now, we'll replace x by 3 into the 1st equation:
3*3 - 2y = 7
9 - 2y = 7 => -2y = 7 - 9 => -2y = -2 => y = 1
The solution of the system is represented by the pair: (3 , 1).
We should use the elimination method because it's the easiest. So first we have to identify the like terms. Which we can see is 2y.
The rule is that if the two terms are the same (-7x and -7x for example then we have to subtract the equation) and if they're different (-2y and 2y for example) we have to add the equation. Doing this we can eliminate y.
Ok so the equation becomes this
+ 4x+2y=14 Now if we add it we get:
7x=21 (the y's cancel out because -2y + 2y is 0)
now to get x on it's own we have to divide it by 7 because currently it's multiplying by it. We do this to both sides. So it becomes:
x=21 divided by 7 (the 7's at the other side cancel each other out)
so we're left with x=3
Now we substitute x into the 1st equation (though u can do it to any, it won't matter) which was 3x-2y=7
3 x 3-2y=7
9-2y=7 ( We want to get y on it's own so we bring the 9 to the other side. Right now's it's positive, when we take it to the other side it will become negative)
-2y=-2 (Now we divide the -2 since it's multyplying. We do it to both sides) We get:
y=-2 divided by -2 which becomes
So the final answer is x=3 and y=1
HOPE IT HELPED :D
Another way to solve the system of equations 3x-2y=7 and 4x+2y=14 is by substitution.
From 3x-2y=7, isolate x as an expression in terms of y.
3x = 7 + 2y
x = (7 + 2y)/3
Substitute this for x in 4x+2y=14
4*(7 + 2y)/3 + 2y = 14
28 + 8y + 6y = 42
14y = 14
y = 1
Now x = (7 + 2*1)/3 = 9/3 = 3
The solution of the system of equations is x = 3 and y = 1
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