Choose an equation that when paired with the equation below, will create a system of equations with infinitely many solutions, one solution, or no solutions.

Accepted Solution

Answer: Infinitely many solutions: [tex]-5x+9y=2[/tex] One solution: [tex]-10x+5y=4[/tex] No solution: [tex]-10x+18y=5[/tex] Step-by-step explanation:  Solve for y from each equation to obtain the equation of the line in slope-intercept form: [tex]y=mx+b[/tex] m: slope b: y-intercept EQUATION ON THE TOP: [tex]-10x+18y=4\\\\y=\frac{5}{9}x+\frac{2}{9}[/tex] Equation 1: [tex]5y=10x+4\\\\y=2x+\frac{4}{5}[/tex] The equation on top and the equation equation 1 has different slopes and different y-intercept, therefore the system will have one solution. Equation 2:  [tex]9y=5x+2\\\\y=\frac{5}{9}x+\frac{2}{9}[/tex] The equation on top and the equation equation 2 are the same, therefore, the system will have infinitely many solutions. Equation 3: [tex]18y=10x+5\\\\y=\frac{5}{9}x+\frac{5}{18}[/tex] The slopes are equal, then both lines will be parallels, therefpre  the system will have no solution.