Question

Solve the system of equations below by graphing.
2.4x -y = -3.5
x^2 + x+y = 6


What are the approximate solutions rounded to the nearest tenth?
(–6.2, –4) and (5, 0.6)
(–4, –6.2) and (0.6, 5)
(–2.4, 2.4) and (3.7, –12.8)
(2.4, –2.4) and (–12.8, 3.7)

Answer 1

First solve for y from the first equation: y = 2.4x + 3.5. Substitute into the second:
x^2 + x + (2.4x + 3.5) = 6 → x^2 + 3.4x - 2.5 = 0.

Solve the quadratic: x = [ -3.4 ± sqrt(3.4^2 + 10) ] / 2 ≈ (-3.4 ± 4.644)/2,
so x ≈ 0.6 or x ≈ -4.0. Then y = 2.4x + 3.5 gives y ≈ 5.0 when x ≈ 0.6 and y ≈ -6.2 when x ≈ -4.0.

So the solutions (rounded to the nearest tenth) are (−4.0, −6.2) and (0.6, 5.0), i.e. the second option.