Can anyone solve this Simultaneous equation?

Question

x + y = 3
3x - 5y = 25

Thanks.

Answer 1

Substitute Method

x + y = 3- - - - - - - -Equation 1
3x - 5y = 25- - - - - Equation 2
- - - - - - - - - -

x + y = 3

x + y - x = - x + 3

y = - x + 3

substitute the y value into equation 2

- - - - - - - - - -

3x - 5y = 25

3x - 5(- x + 3) = 25

3x - (- 5x + 15) 25

3x + 5x - 15 = 25

8x - 15 = 25

8x - 15 + 15 = 25 + 15

8x = 40

8x / 8 = 40 / 8

x = 40 / 8

x = 5

Insert the x value into equation 1

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

x + y = 3

5 + y = 3

5 + y - 5 = 3 - 5

y = - 2

Insert the y value into equation 1
- - - - - - - - -

Check equation 1

x + y = 3

5 + (- 2) = 3

5 - 2 = 3

3 = 3

- - - - - - -

Check equation 2

3x - 5y = 25

3(5) -5(- 2) = 25

15 - (- 10) = 25

15 + 10 = 25

25 = 25

- - - - - - - -

Both equations balance

The solution set { 5, - 2 }

- - - - - - - - - -s-

Answer 2

Three ways come to mind...
One you've already seen, but maybe not the most straight forward.

1) x + y = 3
2) 3x - 5y = 25


Method 2.
Solve one equation for one variable and then substitute into the second equation. Maybe the easiest in this case.
From equation 1, solve for x in terms of y. You could solve for y in terms of x. The only difference would be that you'd get y first.
x + y = 3
Add -x t0 both sides....
y = 3-x

To find x, substitute into Equation 2
3x - 5(3-x) = 25
3x - 15 + 5x = 25
8x=40
Multiplying both sides by -1/8
x = 5

Back a ways we solved for y in terms of x, so substitute 5 for x
y = 2-x
y = 3 - (5) = -2

Check
3x - 5y = 25?
3(5) - 5(-2) = 15+ 10 = 25 YEP RIGHT ANSWERS


Method 3
Matrices
A =
| 1 . . 1 |
| 3 . .-5 |
= (1)(3) - (1)(-5)
= 8

X =
| 3 . . 1 |
|25 ..-5 |
= (25)(1) - (3)(-5) = 25+15
= 40
x = X/A = 5
x=5

Y=
| 1 . . 3 |
| 3 ..25 |
= (3)(3) - (1)(25) = 9-25= -16
Y/A = -16/8 = -2
y = -2
Ah ha... same answers.

Answer 3

multiply the first equation by 5
5x + 5y = 15 and 3x -5 y = 25

add the two equations

8x = 40 divide by 8 x = 5

substitute in the first eq 5 + y = 3
y = 3 - 5 = - 2

x = 5 and y = -2

Answer 4

This is also called a system of equations and you can solve it by graphing, eliminating or substitution and all will give you the correct answer. Let's do substitution here.
x + y = 3
Set the top equation equal to x
x=3 - y
Now that we know what x equals, plug (3-y) in for x in the second equation
3(3-y) -5y=25
Now work it out to solve for y
9-3y-5y=25
9 - 8y=25
-8y=16
y= - 2
Now that we know what y equals, plug in into either equation and solve for x. Let's put it in the top one
x+y=3
x+(-2)=3
x=5
So, the points that satisfy this system of equations is (5, -2)

Hope this helps!

Answer 5

x + y = 3
x = 3 - y
then, subsitute it into the other eq.
3(3 - y) - 5y = 25
9 - 3y - 5y = 25
-8y = 16
y =-2
So,
x = 3 - (-2)
x = 5
Thus,x= 5 , y = -2

Answer 6

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-3x-3y=-9
3x-5y=25
---------------
-8y=16
y=-2
then substitute -2 in for y
x-2=3
x=5

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Answer 7

x = 3 - y
3(3 - y) - 5y = 25
9 - 3y -5y = 25
-3y - 5y = 25 - 9
-8y = 16
8y = -16
y = -2

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

Answer 8

x + y = 3 (eq. 1)
3x - 5y = 25 ( eq. 2)
_________________

x + y = 3 (eq. 1)
x = 3 - y (eq. 3)
________________
substitute eq. 3 to eq. 2
3x - 5y = 25 (eq. 2)
3(3-y) - 5y = 25
9 - 3y - 5y = 25
9 - 8y = 25
9 - 9 - 8y = 25 - 9
- 8y = 25 - 9
-8y = 16
-8y/-8 = 16/-8
y = - 2 ==> value of y
_____________________
Substitute the value of y tp eq. 1
x + y = 3 (eq. 1)
x + (-2) = 3
x - 2 = 3
x - 2 + 2 = 3 + 2
x = 5 ==> value of x
_________________
x = 5
y = -2
___________________

to check;
x + y = 3 (eq. 1)
5 - 2 = 3
3 = 3

3x - 5y = 25 (eq.2)
3(5) - 5(-2) = 25
15 + 10 = 25
25 = 25
_______________
Good luck!!!

Answer 9

the key is subsitution!!
x+y=3 so x=3-y

now lets substitute

3(3-y)-5y=25
9-8y=25
-8y=16
y=(-2)

now plug back into original problem
x+(-2)=3
x=5

Answer 10

x = 5
y = -2

Solve by:
x = 3 - y

then

3 (3 - y) - 5y = 25

then

9 - 3y - 5y = 25

then

9 - 8y = 25

then 9 = 25 + 8y

then

8y = -16

then

y = -2

then

x - 2 = 3