algebra :( :( :(?

Question

Solve these simultaneous equations using an algebraic method.

3x + 7y = 18

x + 2y = 5

Answer 1

Take the second equation and solve for x. x = 5-2y

Substitute for x in the first equation.

3(5-2y) + 7y = 18

15-6y+7y=18
15+y=18
y=3

Now solve for x in either equation by substituting 3 for y.

x+2y=5
x+6=5
x= -1

Answer 2

Substitution Method

3x + 7y = 18- - - - -Equation 1
x + 2y = 5- - - - - - -Equation 2
- - - - - - - - -

isolate the x variable in equation 2

x + 2y = 5

x + 2y - 2y = - 2y + 5

x = - 2y + 5

substitute the x value into equation 1
- - - - - - - - - -

3x+ 7y = - 18

3( - 2y + 5) + 7y= 18

y + 15 = 18

Transpose 15

y + 15 - 15 18 - 15

y = 3

Insert the y value into equation 2

- - - - - - - - - -

x + 2y = 5

x + 2(3) = 5

x + 6 = 5

Transpose 6

x + 6 - 6 = 5 - 6

x = - 1

Insert the x value into equation 2

- - - - - - - - -

Check for equation 2

x + 3y - 5

- 1 + 2(3) = 5

- 1 + 6 = 5

5 = 5

- - - - - - -

Check for equation 1

3x + 7y = 18

3(- 1) + 7(3) = 18

- 3 + 21 = 18

18 = 18

- - - - - - - - - -

Both equations balance

The solution set is { - 1, 3 }

- - - - - - - - -s-

Answer 3

x= -1 y = 3

using substitution method:
3x + 7y =18
x +2y = 5

solve for x in x +2y=5:

x +2y =5, so x =5 - 2y

then sub that x value in 3x + 7y=18

3(5 - 2y) + 7y = 18
15 - 6y + 7y = 18
15 + y = 18
y = 3

use that to solve for x in x + 2y = 5

x + 2 (3) = 5
x + 6 = 5
x = -1


Check your work:

3x + 7y = 18
3(-1) + 7(3) = 18
-3 + 21 = 18
18 = 18 ----> okay

x + 2y = 5
-1 + 2(3) = 5
-1 + 6 = 5
5 = 5 -------> okay

Answer 4

Solve for x in one equation:

x + 2y = 5
x = -2y +5

Substitute this in for x in the other equation:
3(-2y +5) +7y = 18
-6y +15 +7y = 18
y = 18 - 15
y = 3

Substitute for y in either equation:
x + 2(3) = 5
x + 6 = 5
x = -1

Check your answer by substituting in both equations:
3(-1) + 7(3) = 18
-3 + 21 = 18
18 = 18 Check!

-1 +2(3) = 5
-1 + 6 = 5
5 = 5 Check!

x = -1, y = 3

Answer 5

It's called systems of equations. There are many methods. One is substitution.

Isolate a variable

x=-2y+5

Then, substitute that into the other equation

3(-2y+5)+7y=18

Distribute

-6y+15+7y=18

Simplify

y+15=18
y=3

Substitute into the other equation.

x+2(3)=5
x+6=5
x=-1

You can also use this method
-3[x+2y=5]
-3x+-6y=-15

Add the equations

3x+7y=18
-3x+-6y=-15

y=3

Substitute

x+2(3)=5
x+6=5
x=-1

Answer 6

Substitution method:

x = -2y + 5

3(-2y + 5) + 7y = 18
-6y + 15 + 7y = 18
y + 15 = 18
y = 3

x + 2(3) = 5
x = -1

Answer 7

From the second equation:
x = 5 - 2y .............(1)
Substituting this in the first equation:
3(5 - 2y) + 7y = 18
15 - 6y + 7y = 18
y + 15 = 18
y = 3
Substituting this in (1):
x = 5 - 2y = 5 - 6 = -1.

Answer 8

3x + 7y = 18

x + 2y = 5

Subtracting 2y from both sides, the second equation becomes

x = 5 - 2y

Now substitute this into the first equation.

3x + 7y = 18

3(5 - 2y) + 7y = 18
15 - 6y + 7y = 18
y = 3

Subsisute this back into the second equation.

x + 2y = 5
x + 2(3) = 5
x + 6 = 5

x = -1

So x=-1 and y=3 is the solution.

Answer 9

You can use two types of methods, (elimination or substitution). For these two equations I'll use the elimination method and it works like this:

1) multiply the 2nd equation my -3 so you can cancel the 3x on the top.

3x+7y=18
-3(x+2y=5)

3x+7y=18
-3x-6y=-15

Now you cancel 3x and -3x, b/c 3x-3x=0
You're left with:

7y=18
-6y=-15

then, you add 7y+-6y=1y=y
and 18+-15=3

So, y=3

Now you plug y=3 to the 1st or 2nd equation, I'll use the 2nd.

x+2(3)=5
x+6=5
Now subtract 6 from both sides.

x=5-6=-1

So you're aswer will be, (x,y)=(-1,3)
Hope this helps if you have any other questions just write to me.

Answer 10

This is very straight-forward... Start with the 2nd equation and solve for x...

x = 5 - 2y

Now substiture that value back into the 1st equation

3(5-2y) + 7y = 18

Now, expand and simplify

15 - 6y + 7y = 18

or, y = 3... Now just substitute back and solve a linear equation for x...

How's that?

Ron.