Question

What is the solution of 3x+y=9 and 3x minus 5y=15

Answer 1

its -15 instead of -45

y=-1

x= 10/3

Equation 1: 3x + y = 9

Equation 2: 3x - 5y = 15

Multiply -1 to equation 2 to cancel out x

-1(3x -5y = 15)

-3x + 5y = -15

Cancel out x

3x + y = 9

-3x + 5y = -15

6y = -6

y = -1

Substitute y with -1 to solve x

3x + (-1) = 9

3x - 1 = 9

+1 = +1

3x = 10

3x/3 = 10/3

x = 10/3

Answer 2

We can use the elimination method to add the two equations together. Multiply the bottom equation by -1 to eliminate the x variable.

Equation 1: 3x + y= 9
Equation 2: 3x - 5y= 15

STEP 1:
Multiply equation 2 by -1
-1(3x - 5y= 15)
-3x + 5y= -45

STEP 2:
Add the two equations:
3x + y= 9
-3x + 5y= -45

the x variable is eliminated
6y= -36
divide both sides by 6
y= -6

STEP 3:
substitute y=-6 in either equation to solve for x

3x + y= 9
3x + (-6)= 9
3x - 6= 9
3x= 15
x= 5

CHECK:
3x + y= 9
3(5) + (-6)= 9
15 - 6= 9
9= 9

ANSWER: x= 5 and y= -6

Hope this helps! :)