Name: Ann Marie Devereux Who is asking: Student Level: Secondary Question: hi there!!, I guess I have a problem!!! 3x+4y=10 (over) 4x+y=9 2x=5y+3 (over) x=3y+1 please help!!! Maria 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 Thus x = 2 Finally substitute x = 2 into either of the two equations you started with and solve for y. Cheers, Penny Go to Math Central