Solve each linear system by substitution method.
x+2y=7
2x+4y=8
I'm getting stuck. Could some one explain the work out process and what the outcome means?
change the first to x = 7 - 2y
sub that into the second
2x + 4y = 8
2(7-2y) + 4y = 8
14 - 4y + 4y = 8
14 = 8 ???? Wow
When this happens there is no solution
Looking at your equations more closely, ..
divide the second by 2 to get
x + 2y = 8 and the first said
x + 2y = 7 ... contradiction !
What you are looking at is really two straight lines that are parallel, they cannot intersect.
To solve this linear system using the substitution method, follow the steps below:
Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve the first equation for x:
From equation 1: x = 7 - 2y
Step 2: Substitute the expression for x into the other equation. In this case, substitute (7 - 2y) for x in equation 2:
2(7 - 2y) + 4y = 8
Step 3: Simplify and solve the equation:
14 - 4y + 4y = 8
14 = 8
Step 4: Analyze the result:
In this case, we obtained a contradiction (14 = 8), which means there is no solution to this system of equations. The two lines representing the equations are parallel and will never intersect, indicating that there are no common solutions for both equations.
Therefore, the linear system is inconsistent, and there is no solution.
If you encounter an inconsistent result like this, it means that the two equations are contradictory or incompatible with each other. The lines representing the equations are parallel and will never intersect.