Question

Please help! I just need someone to teach me how to solve this!

Answer 1

you have 2 lines, correct?

Answer 2

so a "solution" is a point or points that they share, correct?

Answer 3

so, easy one first... what happens if the lines are parallel?

Answer 4

from geometry: parallel lines never _____.

Answer 5

hold on, graphing is the long and harder way... what happens when you have a 3 dimensional line? not so easy to graph those...

parallel lines never meet, correct. is there something belonging to lines that we can use to tell if they are parallel or not?

Answer 6

oh... well in that case, good job. you didn't mention that in the problem statement.

Answer 7

yeah

Answer 8

so what is an expression for y?

Answer 9

so in the first eqn, substitute in the expression which is equivalent to y. then you'll have only x to deal with.

Answer 10

yep

8x +2(-5x+1) = -2

now solve for x. that is the x coordinate of the solution

Answer 11

no worries... did you solve?

Answer 12

so now, plug that into the y equation (y = -5x+1) and solve for y.

then you'll have the solution point (x, y) except with the numbers you found.

Answer 13

as a check, you can put the solution into both equations and make sure they make true statements...

8(2) + 2(-9) =? -2... yep

-9 =? -5(2) + 1 ... yep

so the solution checks!

Answer 14

no, x =2 and y = -9 so (2, -9)

Answer 15

no worries!!!

Answer 16

how about it?

Answer 17

yeah, i teach math

Answer 18

fisrt is easy... just add the eqns.
left side + left side = right side + right side

doing that should "eliminate" the y variable

Answer 19

4x + y = 8
-3x - y = 0

gives

x = 8 when you add

Answer 20

you can think of it as

(4x + y) + (-3x - y) = 8 + 0

4x + y - 3x - y = 8

4x - 3x + y - y = 8

x + 0 = 8

x = 8

Answer 21

yes but you need to multiply each eqn by a number first...

which variable would you like to eliminate?

Answer 22

pick one

Answer 23

okay, so what are the coefficients on the y's?

Answer 24

coefficient means just the number not the variable... so 2 and -5, they're already opposite in sign, which is good.

what is the least common multiple of 2 and 5?

Answer 25

great, so you want to make the coeffecients on the y variables the same, except opposite in sign.

so if you multiply the first eqn by 5 (that means everything gets multiplied by 5), what is the new eqn?

do the same for the second, except you'll multiply that one by 2.

write the new eqns and add and the y variable should be eliminated.

then solve for x.

Answer 26

should get 15x + 4x = -50 + 6 => 19x = -44

Answer 27

5(3x + 2y = -10) => 15x + 10y = -50
2(2x - 5y = 3) => 4x - 10y = 6

adding them gives

19x + 0 = -44

=> 19x = -44,
correct?

Answer 28

you can add them in columns, it makes it easier

Answer 29

what is confusing you?

Answer 30

sorry, trying to help

once you have 19x = -44, just divide to get x = -44/19

to solve for y you can substitute the value of x into one of the eqns and solve for y or you can eliminate x from the original set of eqns and find y that way.

the choice is yours, but i prefer the latter method. working with fractions can be a bit tedious.