How would you solve y=2x+3 and y=2x-2 using the substitution.
before you even start, did you notice the two equations have the same slope, but have different y-intercepts.
Thus they will never meet, and therefore there can't be a solution.
If you try it anyway ....
first equation:
y = 2x+3
sub in the second
2x-2 = 2x + 3
-2= 3 , mmmhhh, that's a good one!
If silly stuff like happens, then usually you can say , "there is no solution".
But you should still understand why that happens.
I understand. What would be the independent variable and dependent variable? Could you give me a real world situation to explain it.
To solve the given system of equations using the substitution method, we'll follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Step 2: Substitute the expression found in Step 1 into the other equation.
Step 3: Solve the resulting equation for the remaining variable.
Step 4: Substitute the value found in Step 3 back into one of the original equations to find the value of the other variable.
Step 5: Write the solution as an ordered pair (x, y).
Let's solve the system using these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
In this case, both equations are already solved for y in terms of x. We have:
y = 2x + 3 ---(Equation 1)
y = 2x - 2 ---(Equation 2)
Step 2: Substitute the expression found in Step 1 into the other equation.
Since both equations are already solved for y, we can skip this step.
Step 3: Solve the resulting equation for the remaining variable.
Since y = 2x + 3 in both equations, we can set the right-hand sides equal to each other:
2x + 3 = 2x - 2
Step 4: Solve the resulting equation for the remaining variable.
To solve for x, we need to isolate the variable on one side:
2x - 2x = -2 - 3
0x = -5
When we combine like terms and simplify, we get:
0 = -5
Step 5: Write the solution as an ordered pair (x, y).
Since 0 = -5 is a contradiction, it means there is no solution to the system of equations. This means the two lines represented by the equations y = 2x + 3 and y = 2x - 2 are parallel and will never intersect.