4x+22=8x+10 5x+5=5x+4
the original equations and check to show that they can have no
solution. Explain your work.
Equation 1:
4x+22=8x+10
First, let's solve this equation for x.
Subtract 4x from both sides:
22=4x+10
Subtract 10 from both sides:
12=4x
Divide both sides by 4:
x=3
Now let's plug this value of x back into the equation to check if it's correct.
4(3)+22=8(3)+10
12+22=24+10
34=34
So the first equation has a solution which is x=3.
Equation 2:
5x+5=5x+4
Let's solve this equation for x. First, subtract 5x from both sides:
5=4
This equation is not true, because 5 does not equal 4. That means the second equation has no solution and is inconsistent. Since one of the equations has no solution, the system of equations has no solution.