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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)

​ (1, 5)

 Nov 8, 2018
 #1
avatar+4221 
+2

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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