Answer:
(x, y) = (1, 1)
Explanation:
You want to solve this system of equations by elimination:
- 6/5x -3/2y = -3/10
- 1/10x +1/5y = 3/10
Fractions
It is often easier to do the arithmetic using integers instead of fractions. We can eliminate the fractions in these equations by multiplying them by 10.
12x -15y = -3
x +2y = 3
Elimination
Now, we want to combine the equations in a way that makes one of the coefficients of the variables be zero. The x-variables have a simple ratio of 12/1 = 12, so we can eliminate x by subtracting the first equation from 12 times the second.
12(x +2y) -(12x -15y) = 12(3) -(-3)
39y = 39 . . . . . . . . . . . simplify
y = 1 . . . . . . . . . . . divide by 39
Substituting for y in the second equation gives ...
x +2(1) = 3
x = 1 . . . . . . . . subtract 2
The solution is (x, y) = (1, 1).
Check
Using these values in the original equations gives ...
6/5(1) -3/2(1) = -3/10 ⇒ 1.2 -1.5 = -0.3 . . . . true
1/10(1) +1/5(1) = 3/10 ⇒ 0.1 +0.2 = 0.3 . . . . true
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Additional comment
The first equation has a factor of 3 that could be removed to give ...
4x -5y = -1
Then we would only need to multiply by -4 instead of -12 to eliminate the x-variable.
You may notice from our "check" that the equations can be written nicely using decimal numbers. The purpose of any rewrite of the equations is to simplify the arithmetic we need to do, helping to make it easier to see solutions, and reducing possible mistakes.
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