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)

hoiuu
Nov 8, 2018

#1**+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.

tertre
Nov 8, 2018