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The solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)
Simultaneous linear and quadratic equations
From the question, we are to determine the solutions to the given system of equations
The given system of equations are
x + y = 3 ----------- (1)
y = x² - 9 ----------- (2)
From equation (1)
x + y = 3
We can write that
y = 3 - x -------- (3)
Substitute this into equation (2)
y = x² - 9
3 - x = x² - 9
x² +x -3 - 9 = 0
x² +x -12 = 0
Solve quadratically
x² +x -12 = 0
x² +4x -3x -12 = 0
x(x +4) -3(x +4) = 0
(x -3)(x +4) = 0
∴ x -3 = 0 OR x +4 = 0
x = 3 OR x = -4
Now, using equation (3)
When x = 3
y = 3 - x
y = 3 - 3
y = 0
When x = -4
y = 3 - -4
y = 3+4
y = 7
∴ When x = 3, y = 0; and when x = -4, y = 7
Hence, the solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)
Learn more on Solving simultaneous linear and quadratic equations here: https://brainly.com/question/16863577
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