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.
