Well, 50 points total given, 25 points per user and 13 bonus for brainliest
anyway
1. add them equations, the y's will cancel x+2y=4 <span>3x-2y=4 +</span> 4x+0y=8
4x=8 divide by 4 both sides x=2 sub back x+2y=4 2+2y=4 minus 2 2y=2 divide 2 y=1 x=2 y=1 (x,y) (2,1) is solution
2. the solution is where they intersect multiply 2nd equation by 2 and add to first 4x-14y=6 <span>-4x+14y=-6 +</span> 0x+0y=0 0=0 infinite solutions
that is because they are actually the same line the solutions are (x,y) such that they satisfy -2x+7y=-3 or 4x-14y=6 (same equaiton) infinite solutions
3. multiply first equation by 2 and add to first 4x+2y=-6 <span>1x-2y=-4 +</span> 5x+0y=-10
5x=-10 divide by 5 both sides x=-2 sub bac x-2y=-4 -2-2y=-4 add 2 -2y=-2 divide by -2 y=1
x=-2 y=1 (x,y) (-2,1)
4. coincident means they are the same line so
we see that we have to multiply 4 by 2 to get 8 multiply top equation by 2 8x+10y=16 8x+By=C B=10 and C=16
5. a. false, either 0, 1, or infinity solutions change the word 'two' to 'one' or 'zero' or 'infinite', or change 'can' into 'can't'
b.false 'sometimes' to 'always'
c. true
d. false, change 'sometimes' to 'always'
EC total cost=150 TC=childC+adultC TC=3c+5a 150=3c+5a
40 tickets, c+a 40=c+a
the equations are 150=3c+5a and 40=c+a
eliminate multiply 2nd equaton by -3 and ad to first one
150=3c+5a <span>-120=-3c-3a +</span> 30=0c+2a
30=2a divide by 2 15=a
sub back 40=c+a 40=c+15 minus 15 25=c
25 children tickets and 15 adult tickets were sold
ANSWERS:
1. (2,1) is solution
2. infinite solutions
3. (-2,1)
4. B=10 and C=16
5. a. false, change the word 'two' to 'one' or 'zero' or 'infinite', or change 'can' into 'can't'
b.false 'sometimes' to 'always'
c. true
d. false, change 'sometimes' to 'always'
EC the equations are 150=3c+5a and 40=c+a 25 children tickets and 15 adult tickets were sold
Question 1: You should know that the Y on both lines will be crossed out and then you add the X which you will end up with: 4X = 8 X = 8/4 = 2
So, y is: 2 + 2Y = 4 2Y = 2 Y = 1 Answer is: (2,1)
Question 2: what you should do is to solve the second line for Y, then plug the Y in the Y that is in the first line! So Y is equal to: Y = 2/7X - 3/7 Plug it in: 4X - 14( 2/7X - 3/7) = 6 Solve for X: X= 5/3 Now solve for Y: Y= 0.2857142857 (if you out them in the equations you will get 6)
Question 3: Same as the Question 2. Solve for Y. then find the number of X. Then find the answer for Y. Answer: X= -11/4 and Y= .625 :)
Question 4: 4X in the first line, then 8X in the second one. So, you can say that their numbers are multiplied by 2. So, B is 10 and C is 16.
Question 5: a. T b. Always. F c. T d. never. F
3c + 5a = 150 a + c = 40 these two equations can solve the problem! Answer: a = 15 and c= 25 :)
Have a wonderful day! (this question took me more than I expected)
