Solve the system of linear equations using the substitution method.
3x + 3y = 0
-6x + 9y = -10
x + y = 0
so
y = - x
then
-6 x + 9 (-x) = -10
- 15 x = -10
x = 2/3
then
y = - x = -2/3
So Yes
Thanks
My answer to the above system is (2/3, -2/3). Am I right?
To solve the system of linear equations using the substitution method, follow these steps:
Step 1: Choose one equation to solve for one variable in terms of the other variable.
Let's solve the first equation for x:
3x + 3y = 0
3x = -3y
x = -y
Step 2: Substitute the expression for the solved variable into the other equation.
Substitute x = -y into the second equation:
-6x + 9y = -10
-6(-y) + 9y = -10
6y + 9y = -10
15y = -10
Step 3: Solve for the remaining variable.
Divide both sides of the equation by 15:
15y/15 = -10/15
y = -2/3
Step 4: Substitute the value of y back into the expression for x to find its value.
x = -y
x = -(-2/3)
x = 2/3
Therefore, the solution to the system of linear equations is x = 2/3 and y = -2/3.