How many solutions does the system of equations x − y = 7 and y equals the square root of the quantity 3 times x plus 3 end quan
1 answer:
9514 1404 393
Answer:
one solution (11, 4)
Step-by-step explanation:
Both equations describe curves with positive slope. The y-intercept of the line (-7) is less than that of the root function (-2), so the line must intersect the root function in exactly one place. There is one solution.
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Solved in the conventional way, the equation would become a quadratic, with two solutions. One of them is extraneous. (That is why I prefer a graphical solution.)
Given ...
x -y = 7
y = √(3x +3) -2
We can substitute for y to get ...
x -7 = √(3x +3) -2
x -5 = √(3x +3)
x^2 -10x +25 = 3x +3 . . . . . . square both sides
x^2 -13x +22 = 0 = (x -11)(x -2) . . . . . gives solutions x=11, x=2
The value x=2 does not satisfy the equation ...
x -7 = √(3x +3) -2 ⇒ 2 -7 = √(3·2 +3) -2 ⇒ -5 = 1 (false)
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So, Option 3 and 4 are the correct answers.