# Which of the systems of equations below could not be used to solve the following system for x and y? 6x + 4y = 24 -2x + 4y = -10 A 6x + 4y = 24 2x - 4y = 10 B 6x + 4y = 24 -4x + 8y = -20 C 18x + 12y = 72 -6x + 12y = -30 D 12x + 8y = 48 -4x + 8y = -10

Question
Algebra foundations
Which of the systems of equations below could not be used to solve the following system for x and y? $$\displaystyle{6}{x}+{4}{y}={24}$$
$$\displaystyle-{2}{x}+{4}{y}=-{10}$$
$$\displaystyle{A}{6}{x}+{4}{y}={24}$$
$$\displaystyle{2}{x}-{4}{y}={10}$$
$$\displaystyle{B}{6}{x}+{4}{y}={24}$$
$$\displaystyle-{4}{x}+{8}{y}=-{20}$$
$$\displaystyle{C}{18}{x}+{12}{y}={72}$$
$$\displaystyle-{6}{x}+{12}{y}=-{30}$$
$$\displaystyle{D}{12}{x}+{8}{y}={48}$$
$$\displaystyle-{4}{x}+{8}{y}=-{10}$$

2020-12-03
Choice A can be obtained from the given system by multiplying the second equation by —1 so it is equivalent to the given system so it can be used to solve for x and y.
Choice B can be obtained from the given system by multiplying the second equation by 2 so it is equivalent to the given system so it can be used to solve for x and y.
Choice C can be obtained from the given system by multiplying both the frst equation the second equation hy 3 so it is equivalent to the given system so it can be used to solve for x and y.
Choice D cannot be obtained from the given system since only the left side of the seconds equation was multiplied by 2.
So, the correct answer is choice D.

### Relevant Questions

A system of linear equations is given below.
$$2x+4y=10$$
$$\displaystyle-{\frac{{{1}}}{{{2}}}}{x}+{3}={y}$$
Find the solution to the system of equations.
A. (0, -3)
B. (-6, 0)
C. There are infinite solutions.
D. There are no solutions.

Solve for x and y.
3x+12y=-30...(1)
6x+6y=-24...(2)
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To solve this, the first thing I did was find the general solutionto the homogeneous equivalent, and got
$$\displaystyle{c}_{{1}}{e}^{{-{5}\frac{{x}}{{2}}}}+{c}_{{2}}{e}^{{{3}\frac{{x}}{{2}}}}$$
Then i used the form $$\displaystyle{K}{\cos{{\left({w}{x}\right)}}}+{M}{\sin{{\left({w}{x}\right)}}}$$ and got $$\displaystyle-{2.72}{\cos{{\left({5}{x}\right)}}}+{2.56}{\sin{{\left({5}{x}\right)}}}$$ as a solution of the nonhomogeneous ODE
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