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consider the following system of equations. how solutions does it have (infinite, one, or no solutions). explain how you can tell without solving the system. 2y = 12x -6y= 5x - 3

User Ulrich Thomas Gabor
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1 Answer

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22 votes

Looking at the equations

The first step is to name the equation

2y = 12x - 6 -----equation 1

y = 5x -3 --------equation 2

the second step is to obtain the gradient and compare each of the equation to that of the equation of a line y= mx + c

Equation 1

2y = 12x - 6

dividing all through by 2

y = 6x - 3

The gradient, when compared to y = mx + c, is 6

Equation 2

when y = 5x - 3 is compared to y = mx + c

m = 5, so gradient = 5

Since the gradients of the two lines are different

i.e m1 = 6 and m2 = 5

The system of equations have one solution

User Hugo Alves
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