Question

How many solutions does the system of equations have y-6x=-3 and 4y-24x=-16

Answer 1

0 - no solution

Explanation:

`\left\{\begin{array}{ccc}y-6x=-3\\4y-24x=-16\end{array}\right\\\\\text{Divide both sides of the second equation by 4}\\\\(4y)/(4)-(24x)/(4)=(-16)/(4)\\\\y-6x=-4\\\\\text{We have received equations in which the left sides}\\\text{are the same and the right sides are different.}\\\\\bold{CONCLUSION}\\\\\text{The system of equations has no solution.}`

`\left\{\begin{array}{ccc}a_1x+b_1y=c_1\\a_2x+b_2x=c_2\end{array}\right\\\\\text{If}\ a_1=a_2,\ b_2=b_2,\ c_1=c_2,\ \text{then the system of equations}\\\text{ has infinitely many solutions}\\\\\text{If}\ a_1=a_2,\ b_1=b_2,\ c_1\\eq c_2,\ \text{then the system of equations}\\\text{has no solutions}\\\\\text{Other the system of equations has one solution.}`