What is the best approximation of the solution to the system, to the nearest integer values?
( , ) Graph of a System of Linear Equations. Line 1 is x plus 2y equals 10. Line 2 is 2x minus 3y equals negative 9. The lines intersect at about 1.7, 4.1.

x+2y=10 2x-3y=-9

Remember that the point of intersection of two lines is the solution of the system of linear equations. We know from our graph that our lines intersect at the point (1.7, 4.1), so the solution of our system of linear equations is (1.7, 4.1).

Now, to obtain the nearest integer of a decimal, we focus on the number after the decimal point: if the number is five or bigger than five, we add 1 to our integer; if the number is less than five, we keep the integer as it is.

For 1.7

The number after the decimal point is 7. Since 7 is bigger than 5, we add 1 to our integer, so the nearest integer of 1.7 is 2

For 4.1

The number after the decimal point is 1. Since 1 is less than 5, we keep our integer as it is, so the nearest integer of 4.1 is 4