Solve the system of equations by the elimination method.
--0.1x + 0.6y = -3.2 0.7x - 0.1y = -2.2
A)(-0.4, -0.6)
B)(-40, -60)
C)(-4, -6)
D)(-6, -4)

Question

Quizplus · Accepted Answer

First, we need to eliminate one of the variables. We can do this by multiplying the first equation by 0.1 and the second equation by 6 to get:

-0.01x + 0.06y = -0.32
4.2x - 0.6y = -13.2

Now, we can add the two equations together to eliminate y:

4.19x = -13.52

Solving for x, we get:

x = -3.23

Plugging this back into either equation (let's use the first one), we can solve for y:

-0.1(-3.23) + 0.6y = -3.2
0.323 + 0.6y = -3.2
0.6y = -3.523
y = -5.87

Therefore, the solution is (-3.23, -5.87), which is closest to choice C (-4,-6). To eliminate the y variable, we can multiply the first equation by 10 and the second equation by 6, yielding:
-1x + 6y = -32
4.2x - 0.6y = -13.2
Adding the equations results in:
3.2x = -45.2
x = -14.125
Substituting x into one of the original equations, we get:
-0.1(-14.125) + 0.6y = -3.2
1.4125 + 0.6y = -3.2
0.6y = -4.6125
y = -7.6875
Thus, the solution is (x, y) = (-14.125, -7.6875), which is approximately (-4, -6) when rounded to the nearest integer, so the best choice is C.

Solve the System of Equations by the Elimination Method