Muriel says she has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is 3y = 2x – 9. Which could be the other equation?
A system of equations with infinitely many solutions is a system where the two equations are identical. The lines coincide. Anything that is equal to [tex]3y=2x-9[/tex] will work. You could try multiply the entire equation by some number, or moving terms around, or adding terms to both sides, or any combination of operations that you apply to the entire equation.
You could multiply the whole thing by 4.5 to get [tex]13.5y=9x-40.5[/tex]. If you want, you could mix things up and write it in slope-intercept form: [tex]y= \frac{2}{3}x-3[/tex]. The point is, anything that is equivalent to the original equation will give infinitely many solutions x and y. You can test this by plugging in values x and y and seeing the answers!
The attached graph shows that four different equations are really the same.
