If (3x+2y=16) and (3x-y=7), what is the value of (y)?
Answer and explanation
Correct answer: (y=3)
When two linear equations contain the same term with the same coefficient, subtraction can eliminate that term. This is the elimination method. Removing one variable leaves a simple equation in the other variable. After finding that variable, the result can be substituted back if the value of the second variable is also needed. Careful subtraction of every term is essential, including the signs on the right-hand sides.
The equations are
m 3x+2y=16
m and
m 3x-y=7
m. Subtract the second equation from the first:
m (3x+2y)-(3x-y)=16-7
m. The
m 3x
m terms cancel, and
m 2y-(-y)=3y
m, so
m 3y=9
m. Dividing by 3 gives
m y=3
m. Therefore option C is correct. The other choices do not satisfy the difference between the two equations.
Frequently asked questions
What is the correct answer to this question?
(y=3)
Why is this the correct answer?
When two linear equations contain the same term with the same coefficient, subtraction can eliminate that term. This is the elimination method. Removing one variable leaves a simple equation in the other variable. After finding that variable, the result can be substituted back if the value of the second variable is also needed. Careful subtraction of every term is essential, including the signs on the right-hand sides.
The equations are
m 3x+2y=16
m and
m 3x-y=7
m. Subtract the second equation from the first:
m (3x+2y)-(3x-y)=16-7
m. The
m 3x
m terms cancel, and
m 2y-(-y)=3y
m, so
m 3y=9
m. Dividing by 3 gives
m y=3
m. Therefore option C is correct. The other choices do not satisfy the difference between the two equations.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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