Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. {:[3x+5y=-6],[6x+10 y=-12]:} Infinitely Many Solutions No Solutions One Solution

Question

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.  {:[3x+5y=-6],[6x+10 y=-12]:} Infinitely Many Solutions No Solutions One Solution

Bytelearn · Accepted Answer

Analyze Equations: Analyze the system of equations. We have the system: 3x + 5y = -6 6x + 10y = -12 We will check if the second equation is a multiple of the first one.Compare Coefficients: Compare the coefficients of the corresponding variables and the constants. The second equation has coefficients that are exactly twice the coefficients of the first equation (6x is 2 times 3x, 10y is 2 times 5y, and -12 is 2 times -6). This suggests that the second equation might be a multiple of the first.Determine Multiplicity: Determine if the second equation is a multiple of the first. Divide the second equation by 2: (6x + 10y = -12) / 2 3x + 5y = -6 This is the same as the first equation.Conclude Solution: Conclude the type of solution the system has. Since the second equation is a multiple of the first, the two equations are essentially the same line. Therefore, every solution to the first equation is also a solution to the second equation. This means the system has infinitely many solutions.

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. $\newline$ $\begin{array}{c} 3 x+5 y=-6 \\ 6 x+10 y=-12 \end{array}$ $\newline$ Infinitely Many Solutions $\newline$ No Solutions $\newline$ One Solution

Full solution

More problems from Solve one-step multiplication and division equations: word problems

Related topics