What is, x+3y=1

-3×-3y=15
Can you show me the steps, confused?

first equation is the line

y = -(1/3) x + 1/3

second equation (-x-y=5) is the line
y = - x - 5

so
-x-5 = -(1/3)x + 1/3

2/3 x = -16/3
x = -8
then y = 3
-------------------
check
-8+9 = ? 1 yes
+24 - 9 = ? 15 yes

there are lots of other ways, like add the two equations

+1 x + 3 y = 1
-3 x - 3 y = 15
---------------- add
-2 x = 16
x = -8 then go back and get y

or substitute

x = 1 - 3y
use that in the second one
-3(1-3y) -3y=15
-3 + 9 y -3 y = 15
6 y = 18
y = +3 again

the first way is brute force finding where two lines hit

The second way is called "elimination".
The third way is called "substitution".

They are all ways o find the intersection of those lines.

Certainly! Let's solve the system of equations step by step.

Given equations:

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

Step 1: Let's solve Equation 1 for x.

x + 3y = 1
Subtract 3y from both sides:
x = 1 - 3y

Now, we have an expression for x in terms of y.

Step 2: Substitute the expression for x into Equation 2.

-3x - 3y = 15
Replace x with 1 - 3y:
-3(1 - 3y) - 3y = 15
Distribute the -3:
-3 + 9y - 3y = 15
Combine like terms:
6y - 3 = 15

Step 3: Solve the resulting equation for y.

6y - 3 = 15
Add 3 to both sides:
6y = 18
Divide both sides by 6:
y = 3

Step 4: Substitute the value of y back into Equation 1 to find x.

x + 3y = 1
Replace y with 3:
x + 3(3) = 1
x + 9 = 1
Subtract 9 from both sides:
x = -8

Therefore, the solution to the system of equations is x = -8 and y = 3.

To verify this solution, substitute these values into the original equations.