Question

On a coordinate plane, 2 lines intersect around (0.6, 2.2). Use the graph to estimate the solution of the system x+2y=5,−x+3y=6. Which integers is the x-value between?

a) 0 and 1
b) 1 and 2
c) 2 and 3
d) 3 and 4

Answer 1

The correct choice is (a) 0 and 1.

To estimate the solution of the system of equations (x + 2y = 5) and (-x + 3y = 6), we can use the given point of intersection, which is approximately (0.6, 2.2) on the coordinate plane.

Let's substitute these values into the two equations:

For
`\(x + 2y = 5\):`

`\[0.6 + 2(2.2) = 0.6 + 4.4 = 5\]`

For
`\(-x + 3y = 6\):`

`\[-0.6 + 3(2.2) = -0.6 + 6.6 = 6\]`

Both equations are satisfied when we use the coordinates of the point of intersection. This verifies that (0.6, 2.2) is indeed a solution to the system.

Now, looking at the x-value of the point of intersection (0.6), we can estimate which integers the x-value is between. Since 0.6 is between 0 and 1, the answer is:

Therefore, the correct choice is (a) 0 and 1.