im really confused about this question:
2x-3y=21 y=3-x
using substitution method. please help
2x - 3(3-x) = 21
Solve for x, then y.
2x+y=3
x+2y=0
X=2 Y=-1
(2,-1)
To solve this system of equations using the substitution method, you need to isolate one variable in one of the equations and substitute it into the other equation. Let's start solving the system of equations step by step:
Given equations:
1. 2x - 3y = 21
2. y = 3 - x
Step 1: Solve one equation for one variable
Looking at equation 2, you can see that y is already isolated. So, equation 2 is solved for y.
Step 2: Substitute the isolated variable into the other equation
Now, you will substitute the value of y from equation 2 into equation 1.
Replace y in equation 1 with 3 - x:
2x - 3(3 - x) = 21
Step 3: Simplify and solve for the remaining variable
Distribute the -3 to both terms inside the parenthesis:
2x - 9 + 3x = 21
Combine like terms:
5x - 9 = 21
Add 9 to both sides of the equation:
5x = 30
Divide both sides of the equation by 5:
x = 6
Step 4: Substitute the value of x back into one of the original equations
We have found the value of x, so now we need to find the value of y. Substitute x = 6 into equation 2:
y = 3 - 6
y = -3
Step 5: Solution
The solution to the system of equations is x = 6 and y = -3.
Therefore, the system of equations 2x - 3y = 21 and y = 3 - x has a solution of x = 6 and y = -3.