Ok so you're supposed to solve the system by method of substitution. And the problem is:
-2/3x + y = 2
2x - 3y = 6
So i put y= 2/3x into the second equation which looks like:
2x - 3(2/3x + 2) = 6
and then
2x-2x-6=6
So like everything cancels out? So then what do you put as the answer??
Thanks!
so i think its
x=0
then solver y
2(0)-3y=6
y=-2
oh, ok thanks!
welcome
To solve the system of equations using the method of substitution, you correctly substituted y = 2/3x into the second equation, which was a good start. However, there seems to be a slight mistake in the subsequent calculations.
Let's go through the steps again:
Start with the system of equations:
1) -2/3x + y = 2
2) 2x - 3y = 6
We can solve for y in terms of x from equation 1:
-2/3x + y = 2
y = 2 + 2/3x
Now substitute this expression for y in equation 2:
2x - 3(2 + 2/3x) = 6
Apply the distributive property:
2x - 6 - 2x/3 = 6
Combine like terms:
2x - 2x/3 = 12
To simplify the equation further, we need to get rid of the fraction in the second term. Multiply through by 3 to eliminate the fraction:
3(2x) - 3(2x/3) = 3(12)
6x - 2x = 36
4x = 36
Now, solve for x by dividing both sides of the equation by 4:
x = 36/4
x = 9
Now that you have the value of x as 9, substitute it back into either of the original equations to solve for y. Let's use equation 1:
-2/3x + y = 2
-2/3(9) + y = 2
-6 + y = 2
Add 6 to both sides:
y = 2 + 6
y = 8
So the solution to the system of equations is x = 9 and y = 8.
In summary, to solve the system of equations using the method of substitution, you need to:
1. Solve one equation for one variable in terms of the other variable.
2. Substitute the expression for the variable into the other equation.
3. Simplify the resulting equation.
4. Solve for the remaining variable.
5. Substitute the found value back into the original equation to solve for the other variable if needed.
I hope this explanation helps! Let me know if you have any more questions.