2x-5y=3 and -4x+10=-6 is there a solution. Use any method to solve if possible
Multiply first equation by 2. Assuming that y was accidentally eliminated in the second equation.
4x - 10y = 6
-4x + 10y = -6
Adding the two together: 0 = 0.
One equation is just the negative of the other. In other words, if you multiply one equation by -1, you get the other.
To determine if the system of equations has a solution, we need to solve the equations simultaneously and check if the solution satisfies both equations.
Let's start by solving the first equation, 2x - 5y = 3:
Step 1: Simplify the equation by moving the term with x to one side and the constant term to the other side:
2x = 5y + 3
Step 2: Divide both sides of the equation by 2 to isolate x:
x = (5y + 3)/2
Now, let's solve the second equation, -4x + 10 = -6:
Step 1: Simplify the equation by moving the constant term to the other side:
-4x = -6 - 10
-4x = -16
Step 2: Divide both sides of the equation by -4 to isolate x:
x = -16/-4
x = 4
So, we have found the value of x to be 4. Now, let's substitute this value of x into one of the equations to find the corresponding value of y:
Substituting x = 4 into the first equation, we get:
2(4) - 5y = 3
8 - 5y = 3
-5y = 3 - 8
-5y = -5
y = (-5)/(-5)
y = 1
Thus, the solution to the system of equations is x = 4 and y = 1.
To verify the solution, substitute these values into both equations and check if they hold true.