3x-2y=-10 2x+3y=2?

Answer 1

*Solve for "x" or "y" in either equation. Let's solve for "x" in the 1st equation.

First: add "2y" with both sides (when you move a term to the opposite side, always use the opposite sign)....

3x - 2y+ 2y = -10 + 2y
3x = - 10 + 2y

*Isolate "x" on one side --- divide each term by "3"....

3x/3 = - 10/3 + 2y/3
x = -10/3 + 2y/3

Sec: replace "-10/3+2y/3" with the x-variable in the 2nd equation....

2(-10/3+2y/3) + 3y = 2

*Distribute the outer term with the terms in parenthesis....

2(-10/3) + 2(2y/3) + 3y = 2
-20/3 + 4y/3 + 3y = 2
-20/3 + 13y/3 = 2

*Eliminate fractions - multiply the denominator with each term...

(3)(-20/3)+(3)(13y/3)=(3)(2) > Cross cancel "like" terms...
-20 + 13y = 6 > Add 20 with both sides...

-20 + 20 + 13y = 6 + 20
13y = 26

*ISolate "y" on one side --- divide both terms by 13...

13y/13 = 26/13
y = 2

Third: replace "2" with the y-variable in the 1st equation...

3x -2(2) = -10
3x - 4 = -10 > *Add 4 with both sides....
3x - 4 + 4 = -10 + 4
3x = - 6

*Isolate "x" on one side --- divide both terms by "3"...

3x/3 = - 6/3
x = -2

Solution: (-2, 2)

Answer 2

i think you're fixing the device of equations First you would be able to desire to place in writing the two in typical style: 3x + 2y = 10 2x - 3y = 3 with a view to get rid of between the variables, you will would desire to multiply the two equations via constants so as that between the variables will cancel. If we multiply the 1st equation via 3 and the 2nd via 2 we get: 9x + 6y = 30 4x - 6y = 6 Now we are able to upload the two equations and the y variable disappears! 13x = 36 x = 36 / 13 back substituting this value into between the equations we sparkling up for y: 3 * (36/13) + 2y = 10 2y = 10 - 108/13 y = 5 - fifty 4/13 = 11/13 Now we verify in the two equations to be sure the answer is genuine: 3 * (36/13) + 2 * (11/13) = 108/13 + 22/13 = one hundred thirty/13 = 10 this tests! 2 * (36/13) - 3 * (11/13) = seventy two/13 - 33/13 = 39/13 = 3 this tests too! subsequently the respond is x = 36/13 y = 11/13

Answer 3

Multiply first by 3 and 2nd by 2

9x - 6y = -30
4x +6y = 4

13x = -26

x = -2

Substitute, 2x + 3y = 2 -4 + 3y = 2 3y = 6 y = 2

Answer 4

3x - 2y = -10
2x + 3y = 2

I converted the equation into a matrix...

3 -2 -10
2 3 2

I perform these matrix operations...

1. R2 * -1 + R1
2. R1 * -2 + R2
3. R2 / 13
4. R2 * 5 + R1

Then I end up with this matrix...

R1: 1 0 -2
R2: 0 1 2

which means that...

x = -2
y = 2

Answer 5

3x - 2y = -10---------X by 3
2x + 3y = 2-----------X by 2

9x - 6y = -30
4x + 6y = 4---------Add

13x = -26
x = -2

Now 2x + 3y = 2 so:-

-4 + 3y = 2
3y = 6
y = 2

Solution is x = -2 , y = 2