Solve each of the following systems 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
Sorry, it should read
y=-5x+3
Consistent means there is a unique solution. Dependent means the two equations are the same line.
To solve the given system of equations using either addition or substitution, let's first consider the second equation:
y = 5x + 3
We can substitute this expression for y into the first equation:
10x + 2(5x + 3) = 7
Now let's simplify this equation:
10x + 10x + 6 = 7
20x + 6 = 7
Subtract 6 from both sides:
20x = 1
Divide both sides by 20:
x = 1/20
Now that we have found the value of x, we can substitute it back into the second equation to find y:
y = 5(1/20) + 3
y = 1/4 + 3
y = 1/4 + 12/4
y = 13/4
Therefore, the solution to the system of equations is x = 1/20 and y = 13/4.
In this case, a unique solution does exist, so the system is not dependent or inconsistent.