Solve the following system of linear equations. Present your solution as an ordered pair (x,y) 3x + 4y = 11 x - 2y = 7

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to following set of equations for x and y, 3x+4y=11 and x-2y=7.

3x+4y=11...(1)

x-2y=7...(2)

Now (1) - 3*(2)

=> 3x + 4y - 3x + 6y = 11 - 21

=> 10y = -10

=> y = -10/ 10

=> y = -1

Substitute y = -1 in (2)

=> x - 2*(-1) = 7

=> x = 7 - 2

=> x = 5

Therefore the required solution is (5 , -1)

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

3x + 4y = 11 .................(1)

x - 2y = 7 ....................(2)

We are given a system of two equations and two variables.

We will use the substitution method to find x and y values.

First, we will re-write (2).

==> x= 2y+7

Now we will substitute x values in (1).

==> 3x+ 4y = 11

==> 3(2y+7) + 4y = 11

==> 6y + 21 + 4y = 11

==> 10y + 21 = 11

==> 10y = -10

==> y= -1

==> x= 2y+7 = 2*-1 + 7 = 5

==> x= 5

Then, the answer is ( 5, -1).

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve the equations and give the solution in the form of ordered pair (x,y)

3x+4y=11......(1)

x-2y=7...........(2).

Eq(1)+2(Eq2) gives 3x+4y +2(x-2y) = 11+2*7 = 25.

3x+4y+2x-4y = 25.

5x = 25.

x= 25/5 = 5.

We substitute y= 5 in x-2y= 7 and get:

5-2y = 7.

So  -2y = 7-5 = 2.

y = 2/-2 = -1.

So the solution is x= 5 and y = -1

So the slotion in the ordered pair form is (x,y) = (5,-1).

tert's profile pic

tert | Student, Undergraduate | (Level 2) eNoter

Posted on

solve the following system:

3x+4y=11

x-2y=7

Step 1.)

Solve any one of the equations for one variable in terms of the other. By
solving 3x=4y=7 for x, we find

3x=-4y+11, devide this by three so that it become

x=-4y+11/3

Step 2.)
Next, we back-substitute into the equation x-2y=7 as follows

(-4y+11)/3-2y=7

(-4y+11-6y)/3=7......cross multiply

-4y+11-6y=7(3)

-4y+11-6y=21

-4y-6y=21-11

-10y=10.........divide this by 10

y=-1

step 3.)

Now, we have to find the x-coordinate of the point of intersection of the two lines. Back-substituting into the equation 3x+4y=11
, we get

3x+4(-1)=11

3x-4=11

3x=11+4.....divide this by three

x=15/3

x=5

 

 

 

Therefore, the solution to the linear system of equations or the point of intersection
of the two lines is (5,-1).



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