helping solving system of equations

Question

will you please help me solve the following system of equations.

 

1.  3x - 2y = 4

     2x - 5y = 21

 

 

2.  3x + y = 7

     3x + y = 10

 

do not show by elimation, thanks

Answer 1

Hi L;

2.

3x + y = 7

y=-3x+7
3x + y = 10

y=-3x+10

y=y

-3x+7=-3x+10

The -3x on both sides cancels...

7=10

No solutions.

There is an easier way to resolve this.  If you are quickly taking an exam, this is what I would do...

2.

3x + y = 7
3x + y = 10

Both equations are in Standard Form...

Ax+By=C, A>0

Slope is -A/B...

Slope of both is -3/1=-3.

Because these have the same slope, these are either parallel, or the same equation.

y-intercept is C/B.

The y-intercept of the first is 7/1=7.

The y-intercept of the second is 10/1=10.

Because these have the same y-intercept, these are parallel and different equations.

No solutions.

One more point...

2.

3x + y = 7
3x + y = 10

Suppose the second equation is presented as...

6x+2y=20-------both sides are doubled.

It would also be easier to establish slope, then y-intercept, to understand how these are or are not related.

Answer 2

1. Solve, but "do not show by elimination"

 

3x - 2y = 4
2x - 5y = 21

 

Solve both equations for y:

 

y = (3x – 4)/2

y = (2x – 21)/5

 

Substitute (3x – 4)/2 for y:

 

(3x – 4)/2 = (2x – 21)/5

 

Multiply both sides by 10:

 

15x – 20 = 4x – 42

 

Add -4x + 20 to both sides:

 

11x = –22

 

x = –2

 

y = (3(–2) – 4)/2 = –5

 

check:

 

3(–2) – 2(–5) =? 4

–6 + 10 = 4 √

 

2(–2) – 5(–5) =? 21

–4 + 25 = 21 √

2. Solve, but "do not show by elimination"

 

3x + y = 7
3x + y = 10

Notice the the left sides are identical; only the constant term on the right is different. This means that they are parallel lines (same slope, different y-intercepts), so there is no solution.

Answer 3

1. you multiply first equation by2 and the second  equation  by 3you will have

6x-4y=8

6x+3y=63

then subtract equation 2 from equation1

-7y=55 then divide both sides by-7

then y=-55/7

we find the value of x from one of the original equations

we will use equation 1

3x-2*55/7=4

3x -110/7=4

add 110/7 for both sides

3x=4+110/7

3x=138/7

divide both sides by3

x=138/21

the solution for this system is(138/21,-55/7 )