Systems of Equations
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Practice questions on Systems of Equations
(See the attached questions file).
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Solution Summary
Neat and step-by-step solutions to all practice questions on systems of equations. Graphs (if any) are included.
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The solution file is attached.
(1) 3(-2) - 4 = -10 and 4(-2) + 3(-4) = -20
Both the equations are satisfied
∴ (-2, -4) is a solution.
(2) From the first equation x = 53 - 9y
Plug this into the second. Then
2(53 - 9y) + 9y = 52
106 - 9y = 52
9y = 54 ==> y = 6 and x = 53 - 9(6) = -1
The solution is (x, y) = (-1, 6)
(3) Multiply the first equation by 4 and add up with the negative of the second. Then
4x + 8y + (-4x - 3y) = 48 + (-18)
5y = 30 ==> y = 6
From the first equation, x = 12 - 2y = 12 - 2(6) = 0
The solution is (x, y) = (0, 6)
(4) x + y = 2 and x + y = 5 ==> 2 = 5 (False)
∴ The system is inconsistent
(5) Multiply the first equation by 2 and add up with the second.
4x - 2y - 4x + 2y = 10 - 18 ==> 0 = -8 [False)
∴ The system is inconsistent
(6) Let the daily fee be x and mileage fee be y
Then we have
3x + 300y = 156 and 5x + 600y = 284
Subtract the second ...
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