Solve the following systemof equations
x + 3y = 9
x = 4 - 3y
I didn't mention...
Is the solution an ordered pair or is there no solution
(4-3y) + 3y = 9
solve for y!
then plug the y value into
x=4-3y
solve for x!
you tell me. does y= a number? then, yes, it's an ordered pair
-3y and postive 3y cancel each other out, leaving 4 = 9, which is false.
So that means that there is not solution?
To solve this system of equations, we will use the method of substitution. Here's how to do it step-by-step:
Step 1: Solve one equation for one variable in terms of the other variable.
From the second equation, we have:
x = 4 - 3y
Step 2: Substitute the expression found in step 1 into the other equation.
Substituting x = 4 - 3y into the first equation, we get:
(4 - 3y) + 3y = 9
Step 3: Simplify and solve for the remaining variable.
Simplifying the equation:
4 - 3y + 3y = 9
4 = 9
Step 4: Analyzing the result:
In step 3, we found that the equation 4 = 9 is inconsistent. This means that the system of equations has no solution. The two equations represent parallel lines that never intersect.
Therefore, the system of equations is inconsistent and has no solution.