Solve the following system of two equations.
-x+7y=10
2x-14y=1
double the first, then add them
-2x + 14y = 20
2x - 14y = 1
0 = 21, which is false, so there is no solution, you have 2 parallel lines that
do not intersect
To solve the system of equations -x + 7y = 10 and 2x - 14y = 1, we can use the method of substitution.
Step 1: Solve one equation for a variable in terms of the other variable.
Let's solve the first equation for x:
-x + 7y = 10
x = 7y - 10
Step 2: Substitute the expression for x into the second equation.
2(7y - 10) - 14y = 1
14y - 20 - 14y = 1
-20 = 1
Step 3: Simplify the equation from step 2.
The equation -20 = 1 is not true, which means there is no solution to the system of equations.
Hence, the given system of equations is inconsistent and has no solutions.