Question 100180: How can I do this?
In the following system of linear equations, state how to combine the two equations to obtain one equation with only one variable.
5x - 4y = 6
2x + 3y = 2
a. Multiply the terms in the first equation by 3, the terms of the second equation by 4, and then add the equation.
b. Multiply the terms in the first equation by 2, the terms of the second equation by 5, and then add the equations.
c. Multiply the terms in the first equation by -3, the terms of the second equation by 4, and then add the equations.
d. Add the equations
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The solution is found by applying the choices given.
a. By inspection, you can see that the variable y can be eliminated by adding the equations, provided you multiply the first equation by 3 and the second equation by 4. (We're actually getting at the least common multiple of 4 and 3, which is 12.)
3(5x - 4y = 6) becomes 15x - 12y = 18
4(2x + 3y = 2) becomes 8x + 12y = 8
Adding the equations, we obtain: 23x = 26, which is one equation with one variable. So, "a" is clearly the answer.
At this point, you are done. The other choices have to be wrong. However, if one of the choices were to be "All of the above" you have to test at least one more alternative.
b. This choice calls for multiplying the terms in the first equation by 2, the terms of the second equation by 5, which is a good start. But it unravels when it concludes "and then add the equations." To eliminate the x-terms, you would need to subtract the equations, not add.
c. This choice calls for multiplying the terms in the first equation by -3, the terms of the second equation by 4, and then adding the equations.
-3(5x - 4y = 6) becomes -15x + 12y = -18
4(2x + 3y = 2) becomes 8x + 12y = 8
When you add them, you do not eliminate a variable, so this choice is wrong.
d. Adding the equations does not eliminate a variable.
5x - 4y = 6
2x + 3y = 2
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7x - y = 8
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