system equation?

Question

solve

2x+3y=8
x-2y=-3

show working please

Answer 1

Okay, let's start by finding a value of x in terms of y. That will be like x=something with a y in it. That way we can "plug in" the value of x into the other equation and get a result for y. Then we can find x. Let's start. The second equation looks easier to solve for x because you don't have to divide anything.

x-2y=-3

Add 2y to both sides
x=2y-3

Now plug 2y-3 in for x in the first equation, and we get

2x+3y=8
2(2y-3)+3y=8

Use distributive property, simplify
4y-6+3y=8

Combine like terms.
7y-6=8

Add 6 to both sides
7y=14

Divide both sides by 7
y=2

We now have a value for y. Let's plug it into one of the equations:

x-2y=-3
x-2(2)=-3

Simplify and solve
x-4=-3
x=-3+4
x=1


x=1
y=2
That is your answer.

Hope this helps.

Answer 2

2x + 3y = 8 - - - - - - -Equation 1
x - 2y = - 3- - - - - - - Equation 2
- - - - - - - -

Substitute Method equation 2

x -2y = - 3

x - 2y + 2y = - 3

x = - 3 + 2y

Insert the x value into equation 1

- - - - - - - - - - - - - -

2x + 3y = 8

2(- 3 + 2y) + 3y = 8

- 6 + 4y +3y = 8

- 6 + 7y = 8

- 6 + 7y + 6 = 8 + 6

7y = 14

7y/7 = 14/7

y = 2

The answer is y = 2

Insert the y value into equation 2

- - - - - - - - - - - - - - - - - - - - - --

x - 2y = - 3

x - 2(2) = - 3

x - 4 = - 4

x - 4 + 4 = - 4 + 4

x = 1

The answer is x = 1

Insert the x value into equation 2

- - - - - - - - - - - - - - - - - - - - - - -


Check for equation 2

x - 2y = - 3

1 - 2(2) = - 3

1 - 4 = - 3

-3 = - 3

- - - - - - - -

Check for equation 1

2x + 3y = 8

2(1) + 3(2) = 8

2 + 6 = 8

8 = 8

- - - - - - - - - - -

The solution set is { 1, 2 }

- - - - - -s-

Answer 3

x - 2y = -3
x = 2y - 3

2x + 3y = 8
2(2y-3) + 3y = 8 (substituting 2y-3 in for x)
4y - 6 + 3y = 8
7y - 6 = 8
7y = 14
y = 2

x = 2y-3 = 2(2)-3 = 1

Answer 4

2x + 3y = 8

AND

x - 2y = -3

First, take and solve for x:
x - 2y = -3
x = -3 + 2y

Second, plug this into the first equation to solve for y.

2x + 3y = 8
2(-3 + 2y) + 3y = 8
-6 + 4y + 3y = 8
7y = 14
y = 2

Third, take this value of y and plug it into either one of the formulas to solve for x.

2x + 3y = 8
2x + 3(2) = 8
2x + 6 = 8
2x = 2
x = 1

Or...

x - 2y = -3
x - 2(2) = -3
x - 4 = -3
x = 1

x = 1
y = 2

Hope this helps!

**Note: Aegor R decided to edit his answer (that had absolutely no work, mind you) after everyone else took their time to respond to your question completely.

Answer 5

2x+3y=8
x-2y=-3
Multiply 2nd equation by -2 getting
-2x +4y= 6
Now add this new equation to the 1st equation getting
7y=14
y=2
Now plug y = 2 into the second equation getting;
x-(2)(2)=-3
x-4=-3
x=1

Answer 6

2x+3y=8
2x-4y=-6 (2)*2
subtracting
7y=14
y=2
substituting
2x+6=8
2x=2
x=1

Answer 7

2x + 3y = 8
-( x - 2y = -3)*2
---------------------
0x + 7y = 14

so, y = 2

Then:
2x + 3(2) = 8
=> 2x = 2
=> x=1