What is the solution for 5x+7y--6 and x+8y=12?
2 answers:
5x+7y=6 and x+8y=12 multiply the 5 coefficient by opposite of x value so. -5(x+8y)=-5×12. Simplify to get -5x-40y=-60. Now add the two equations to eliminate x. 5x+7y=6 + -5x-40y=-60. Equals -33y=-66 Now solve for y by dividing -33 on both sides . Y= 2. Now substitute your answer for y into one of the origibal equations to find x . X+8(2)=12 Now solve x+16=12 Now move 16 to right side .x= -16+12 . Solve to get x= -4. So now you have your answer for x and y (-4,2) .
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Answer:
n = 10
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
=
[ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 12 and d = 5 and = 345, thus
[ (2 × 12) + 5(n - 1) ] = 345 ( multiply both sides by 2 )
n( 24 + 5n - 5) = 690 ← distribute and simplify left side
n(19 + 5n) = 690
19n + 5n² = 690 ( subtract 690 from both sides )
5n² + 19n - 690 = 0 ← in standard form
(5n + 69)(n - 10) = 0 ← in factored form
Equate each factor to zero and solve for n
5n + 69 = 0 ⇒ 5n = - 69 ⇒ n = -
n - 10 = 0 ⇒ n = 10
However, n > 0 , thus n = 10