-7x+2y=13
-14+4y=26
Is this no solution? (0,0)
no solution. I have no idea what you mean by 0,0...that would indicate a solution..
I assume you have a typo, and the 2nd equation is
-14x + 4y = 26
notice dividing by 2 will yield the first equation
so you basically have ONE equation in TWO unknowns, which will yield an infinite number of solutions,
e.g. (1, 10) is one,
so is (13, 52) etc
To determine if the system of equations has no solution, we need to check if the two equations are consistent or inconsistent. If they are inconsistent, then the system has no solution.
Let's solve the system of equations to find out:
Equation 1: -7x + 2y = 13
Equation 2: -14 + 4y = 26
First, let's solve Equation 2 for y:
-14 + 4y = 26
Add 14 to both sides:
4y = 26 + 14
4y = 40
Divide both sides by 4:
y = 40/4
y = 10
Now substitute the value of y into Equation 1 to solve for x:
-7x + 2(10) = 13
-7x + 20 = 13
Subtract 20 from both sides:
-7x = 13 - 20
-7x = -7
Divide both sides by -7:
x = -7/-7
x = 1
So the solution to the system of equations is x = 1 and y = 10.
Since there is a unique solution, (1, 10), the system of equations does not have no solution. Therefore, (0, 0) is not the solution.