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Which of the ordered pairs of numbers (c, d) satisfies the simultaneous equations shown?
\(c+2d=6\)
\(-3c-6d=-18\)
A (-2, 4)
B (-1, -3)
C (0, 2)
D (2, 1)
E (3, -9)
\(c+2d=6\)
\(-3c-6d=-18\)
A (-2, 4)
B (-1, -3)
C (0, 2)
D (2, 1)
E (3, -9)
kungfury42
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02 Feb 2022, 02:36
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Quick glance tells us that these are not 2 different equations but just one equation and the same one again multiplied by a coefficient on both sides.
Since these are essentially the same equations, it reduces our efforts to just finding which point out of the given options satisfies the first (and the simpler looking) equation.
Substituting option A in equation 1 we get:
-2+2*4 = -2+8 = 6 which is equal to the RHS
Hence, our answer is (-2, 4) option A.
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Since these are essentially the same equations, it reduces our efforts to just finding which point out of the given options satisfies the first (and the simpler looking) equation.
Substituting option A in equation 1 we get:
-2+2*4 = -2+8 = 6 which is equal to the RHS
Hence, our answer is (-2, 4) option A.
Posted from my mobile device
07 Feb 2022, 10:02
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Bunuel
Which of the ordered pairs of numbers (c, d) satisfies the simultaneous equations shown?
\(c+2d=6\)
\(-3c-6d=-18\)
A (-2, 4)
B (-1, -3)
C (0, 2)
D (2, 1)
E (3, -9)
Before we try to solve the given system of equations, we might first consider whether the system can be solved at all. \(c+2d=6\)
\(-3c-6d=-18\)
A (-2, 4)
B (-1, -3)
C (0, 2)
D (2, 1)
E (3, -9)
Remember that, if the two equations are identical, then there will be infinitely many solutions to the system.
Notice that, if we take the top equation, \(c+2d=6\), and multiply both sides by -3, we get: \(-3c-6d=-18\), which is the same as the bottom equation.
Since our two equations are identical, there are infinitely many solutions to the system.
This means, we'll have to test each answer choice to see whether it lies on either of the equations.
A (-2, 4)
Let's see if c = -2 and d = 4 is a solution to the top (easier-to-use) equation by plugging them into the equation.
We get: \((-2)+2(4)=6\). It WORKS!!
Answer: A
