Homework Help

Solve the system of equations 3x-2y=7 and 4x+2y=14?

user profile pic

loochy | Student | (Level 2) eNoter

Posted May 31, 2011 at 3:35 PM via web

dislike 0 like

Solve the system of equations 3x-2y=7 and 4x+2y=14?

3 Answers | Add Yours

user profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted May 31, 2011 at 3:38 PM (Answer #1)

dislike 0 like

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).

user profile pic

ridhamc | Student, Grade 9 | eNotes Newbie

Posted May 31, 2011 at 8:18 PM (Answer #2)

dislike 0 like

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.

3x-2y=7

4x+2y=14

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

3x-2y=7

+  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

We get

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=7-9

-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

y=1

So the final answer is x=3 and y=1

HOPE IT HELPED :D

 

user profile pic

tonys538 | TA , Undergraduate | (Level 1) Valedictorian

Posted November 1, 2014 at 5:56 AM (Answer #3)

dislike 0 like

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

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes