4x+22=8x+10 5x+5=5x+4
the original equations and check to show that they can have no
solution. Explain your work.
We will solve the two original equations to find their solutions and check if they have solutions:
1) 4x + 22 = 8x + 10
Subtract 4x from both sides of the equation:
22 = 4x + 10
Subtract 10 from both sides of the equation:
12 = 4x
Divide both sides by 4:
x = 3
So for the first equation, x = 3 is the solution.
2) 5x + 5 = 5x + 4
Subtract 5x from both sides:
5 = 4
This statement (5=4) is not true, which means there is no solution for the second equation.
Since the second equation does not have a solution, the system of these two equations will also have no solution.
Explanation: A system of linear equations has no solution if the lines represented by the equations are parallel or if they are the same lines, but the second equation has no solution because it is a contradictory statement. This means that there is no value of x that will make that equation true, so it cannot have a solution.