How many solutions does this system of equations have ??
2x= 10y + 6 and x+ 5y = 3
two?
@damon can you help please.
x = +5 y + 3
x = -5 y + 3
-----------------add
2 x = 6
x = 3
then y = 0
they cross at
(3,0)
@damon so how many solutions ?
one
Thank you @damon.
To determine the number of solutions for a system of equations, we can use the method of substitution or elimination.
Let's start with the first method, substitution:
1. Solve one equation for a variable in terms of the other variable.
- From the second equation, solve for x: x = 3 - 5y.
2. Substitute the expression for the variable into the other equation.
- In this case, substitute x in the first equation: 2(3 - 5y) = 10y + 6.
3. Simplify and solve the resulting equation.
- Distribute 2 to the expression: 6 - 10y = 10y + 6.
- Move the terms to one side: -10y - 10y = 6 - 6.
- Combine like terms: -20y = 0.
- Divide both sides by -20: y = 0.
4. Substitute the found value of y back into either of the original equations to solve for the other variable.
- In this case, substitute y = 0 into the second equation: x + 5(0) = 3.
- Simplify: x + 0 = 3.
- Therefore, x = 3.
After solving, we find that the system of equations has a unique solution: x = 3, y = 0.
Thus, the system of equations has exactly one solution.