Solve the following system by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent.
10x+2y=7
y=-5x+3
no solution.
first you have to place the -5x on the same side as the y... and it becomes a positive
5x+y =3
then you multiply it by -2
-2(5x+y =3)
then it is -10x-2y =-6
add it to 10x+2y = 7
you will see that 0 does not = 1, so therefore it has NO SOLUTION
as to whether its dependent or inconsistent... uhm, there should be something in the text that explains that :]
The equations are inconsistent. Both cannot simultaneously be true.
To solve the given system of equations using either addition or substitution, we can first substitute the value of y from the second equation into the first equation. Then we can solve for x.
Given the system of equations:
1) 10x + 2y = 7
2) y = -5x + 3
Substituting the value of y from the second equation (y = -5x + 3) into the first equation, we have:
10x + 2(-5x + 3) = 7
Now we can solve for x:
10x - 10x + 6 = 7
6 = 7
Since 6 is not equal to 7, this means that the system of equations is inconsistent. This indicates that the system does not have a unique solution.
Therefore, the solution to the given system is inconsistent.