A system of equations is graphed on a coordinate plane.

2x+3y=12, 4x+2y=10

Which coordinates are the best estimate of the solution to the system of equations?

(6, 0)

(0, 5)

(1, 4)

‚Äč (1, 5)

 Nov 8, 2018

First, let's try to solve the system of equations; 2x+3y=12, 4x+2y=10.


If we find the LCM of 2 and 4, which is 4, we can multiply the entire first equation by 2.


Therefore, 4x+6y=24 and 4x+2y=10.


In this process of elimination, we can subtract the first equation from the second equation.


Doing so, we get 4y=14, and y=14/4 or y=7/2 (3.5).


We just plug the value of y in the equations, to solve for the value of x.


Again, doing so, we get 2x+3(3.5)=12, 2x+10.5=12, 2x=1.5, x=0.75.


Now that we have solved for the value of x and y, we can put in parenthesis. 


So, we have (0.75, 3.5), which rounds to (1, 4) or the third option. 

 Nov 8, 2018

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