Name: Ann Marie Devereux
Who is asking: Student
Level: Secondary

hi there!!, I guess I have a problem!!!

  • 3x+4y=10 (over)

  • 2x=5y+3 (over)

please help!!!

Hi again Maria,

Lets consider the first problem. This pair of equations is called a system of linear equations (system because there is more than one and linear because the graph of each equation is a line in the plane). What you are looking for is a pair of numbers x and y that satisfy both equations. Geometrically you are looking for the coordinates of the point where the two lines intersect.

The standard technique to solve such a pair of equations is to find an equivalent pair of equations that have the same coefficient for one of the variable. What I plan to do is to multiply both sides of the second equation by 4 and this will result in 4 being the coefficient of y in this equation. Hence I will have two equations, both of which have 4 as the coefficient of y.

3x + 4y = 10
4x + y = 9

3x + 4y = 10
4(4x + y) = 4(9)

 3x + 4y = 10
16x + 4y = 36

Now subtract the first equation from the second equation

16x + 4y -(3x + 4y) = 36 - 10

13x = 26


x = 2

Finally substitute x = 2 into either of the two equations you started with and solve for y.


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