A few days ago

this is one of my math problems… i need some help?

Without graphing, tell which pair(s) of equations below will make a system of equatoins with ONE solution.

How do you know?

A. 5X-Y=3 B. 3Y-6X= -12 C. 3Y+2=6X

THANKS a bunch.

Top 2 Answers
A few days ago

Favorite Answer

make y the subject of each equation.

A. 5X-Y=3 –> Y = 5X – 3

B. 3Y-6X= -12 –> Y = 6X/3 -12/3 = 2X – 4

C. 3Y+2=6X –> Y = 6X/3 – 2/3 = 2X -2/3

all of these equations are in the form y= mx + b , where m tells you the gradient (slope) of the line.

>> if the gradient is the same then the lines are parallel, if the gradient is not the same then they will intersect (so there will be ONE solution)

so the gradients of the equations are

A. 5

B. 2

C. 2

because B and C have the same graident ( m = 2) they are parallel so there will be no solutions (they don’t intersect).

all of the other lines have different gradients so this means they will intersect at only one point

>> therefore A and B will have one solution and A and C will have one solution.


A few days ago
A & B and A & C. They are lines with different slopes and will intersect at only one point. B and C have the same slopes and are therefore parallel (no solutions)