Solve y = 2x + 1 and x + y = 10 by substitution.
Answer and explanation
Correct answer: (3, 7)
The answer is C, (3,7). Substitution means replacing a variable in one equation by an expression equal to that variable. Since y=2x+1, put 2x+1 in place of y in x+y=10. This gives x+(2x+1)=10, so 3x+1=10, 3x=9, and x=3. Now substitute x=3 into y=2x+1: y=2(3)+1=7. Therefore the ordered pair is (x,y)=(3,7). Check both original equations: 3+7=10 and 7=2(3)+1, so the pair is correct. A gives 2+8=10 but 8 is not 2(2)+1. B and D also fail at least one equation. Always check both equations because satisfying only one is not enough.
Frequently asked questions
What is the correct answer to this question?
(3, 7)
Why is this the correct answer?
The answer is C, (3,7). Substitution means replacing a variable in one equation by an expression equal to that variable. Since y=2x+1, put 2x+1 in place of y in x+y=10. This gives x+(2x+1)=10, so 3x+1=10, 3x=9, and x=3. Now substitute x=3 into y=2x+1: y=2(3)+1=7. Therefore the ordered pair is (x,y)=(3,7). Check both original equations: 3+7=10 and 7=2(3)+1, so the pair is correct. A gives 2+8=10 but 8 is not 2(2)+1. B and D also fail at least one equation. Always check both equations because satisfying only one is not enough.
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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