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lukranit [14]
3 years ago
9

Choose an equation that when paired with the equation below, will create a system of equations with infinitely many solutions, o

ne solution, or no solutions.

Mathematics
1 answer:
Alchen [17]3 years ago
4 0

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

<u>EQUATION ON THE TOP:</u>

-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.

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