Answer:
- multiply the second equation by -2
- (x, y) = (2, 2)
Explanation:
Apparently, you want to solve the system of equations by multiplying or dividing one of them by a factor that will make the y-coefficients the same.
Multiplication
The y-coefficients are 2 and -1, so we can multiply the first by -1/2 to make it the same as the second, or we can multiply the second by -2 to make it the same as the first.
We prefer to work with integers, rather than fractions, so we choose to multiply the second equation by -2.
-2(3x -y) = -2(4)
-6x +2y = -8 . . . . . . . y-coefficient is the same as in the first equation
Solution
Now, we can subtract the second equation from the first to eliminate the y-terms:
(3x +2y) -(-6x +2y) = (10) -(-8)
9x = 18 . . . . . . . . . simplify
x = 2 . . . . . . . . . divide by 9
Substituting this into the original second equation gives ...
3(2) -y = 4
6 -4 = y = 2 . . . . . . . add (y-4)
The solution is (x, y) = (2, 2).
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Additional comments
The picture posted here has no question, so there is no way to tell how to answer it. Any answer must be provided in accordance with whatever instructions are given.
Solving these equations is somewhat easier if you make the y-coefficients opposites, rather than the same. This can be done by multiplying the second equation by 2: 6x -2y = 8. Now the equations can be added to give 9x = 18, as above.
Of course, the x-coefficients are already the same, so we can more easily eliminate the x-terms. Subtracting the second equation from the first gives ... (3x +2y) -(3x -y) = (10) -(4), or 3y = 6.