Question

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.

Answer 1

Answer:

Infinitely many solutions: $-5x+9y=2$

One solution: $-10x+5y=4$

No solution: $-10x+18y=5$

Step-by-step explanation:

 Solve for y from each equation to obtain the equation of the line in slope-intercept form:

$y=mx+b$

m: slope

b: y-intercept

EQUATION ON THE TOP:

$-10x+18y=4\\\\y=\frac{5}{9}x+\frac{2}{9}$

Equation 1:

$5y=10x+4\\\\y=2x+\frac{4}{5}$

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:

 $9y=5x+2\\\\y=\frac{5}{9}x+\frac{2}{9}$

The equation on top and the equation equation 2 are the same, therefore, the system will have infinitely many solutions.

Equation 3:

$18y=10x+5\\\\y=\frac{5}{9}x+\frac{5}{18}$

The slopes are equal, then both lines will be parallels, therefpre  the system will have no solution.