A system of equations is graphed on a coordinate plane.
Which coordinates are the best estimate of the solution to the system of equations?
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.