Question
If minus, x, plus, 9, y, equals, minus, 5−x+9y=−5 and 6, x, minus, 7, y, equals, 36x−7y=3 are true equations, what would be the value of minus, 7, x, plus, 16, y−7x+16y?
Answers
Answered by
GPT 3.5
To solve the given equations, we can use the method of substitution.
From the first equation, -x + 9y = -5,
we can rearrange it to express x in terms of y: x = 9y - 5.
Now we substitute this expression for x in the second equation:
6(9y - 5) - 7y = 3.
Simplifying this equation gives:
54y - 30 - 7y = 3,
47y = 33,
y = 33/47.
Substituting this value of y back into the expression we want to evaluate:
-7x + 16y = -7(9y - 5) + 16y = -63y + 35 + 16y = -47y + 35.
Finally, we substitute the value of y we found:
-47(33/47) + 35 = -33 + 35 = 2.
Therefore, the value of -7x + 16y is 2.
From the first equation, -x + 9y = -5,
we can rearrange it to express x in terms of y: x = 9y - 5.
Now we substitute this expression for x in the second equation:
6(9y - 5) - 7y = 3.
Simplifying this equation gives:
54y - 30 - 7y = 3,
47y = 33,
y = 33/47.
Substituting this value of y back into the expression we want to evaluate:
-7x + 16y = -7(9y - 5) + 16y = -63y + 35 + 16y = -47y + 35.
Finally, we substitute the value of y we found:
-47(33/47) + 35 = -33 + 35 = 2.
Therefore, the value of -7x + 16y is 2.