Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Help with math problems (Urgent!)?

Solve this equation by graphing, substitution, and the addition method, and show work.

2x+3y=6

x-2y=10

15 Answers

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  • 1 decade ago
    Best Answer

    GRAPHING:

    When you graph you have to put the equation into y = mx + b

    m is slope, b is the y-intercept.

    slope is rise over run. so if you have 1/2x, then you rise (up) 1, and run (go right) 2.

    y-intercept is the place where a point crosses on the y axis.

    for help on graphing this is a good site - > http://education.yahoo.com/homework_help/math_help...

    (check out number 15 and the ones after. this sight tells you step by step how to do things, it's very useful for any math problems).

    equation # 1- 2x + 3y = 6

    (subract 2x from both sides)

    3y = -2x + 6

    (divide by 3 on each side)

    y = -2/3x + 6/3

    (simplify)

    y = -2/3x + 2

    equation # 2- x - 2y = 10

    (add x to both sides)

    - 2y = -x + 10

    (divide by -2 on both sides)

    y = -1/-2x + 10/-2

    (there is a "1" understood with "x", that is why it's -1/-2x. Now simplify)

    y = 1/2x + 5

    (remember - negative divided by a negative is positive)

    SUBSTITUTION:

    equation # 1- 2x + 3y = 6

    equation # 2- x - 2y = 10

    Choose which variable you want to solve for.

    I think the x in equation 2 would be easiest, so here we go:

    x - 2y = 10

    (add 2y to both sides)

    x = 2y + 10

    Now substitute it in for equation # 1

    2x + 3y = 6

    2 (2y + 10) + 3y = 6

    (distribute)

    4y + 20 + 3y = 6

    (combine like terms)

    7y + 20 = 6

    (subtract 20 from each side)

    7y = -14

    (divide by 7 on each side to isolate y)

    y = -14/7

    (simplify)

    y = -2

    Now substitute y in either original equation to solve for x.

    I'm putting it back into equ. # 1

    equation # 1- 2x + 3y= 6

    2x + 3(-2)=6

    2x + -6 = 6

    (add 6 to each side)

    2x = 12

    (divide by 2 on each side)

    x = 6

    ADDITION METHOD:

    (here is a site that might help you understand this better, http://www.jamesbrennan.org/algebra/systems/additi...

    equation # 1- 2x+3y=6

    equation # 2- x-2y=10

    2x + 3y= 6

    (x - 2y= 10) Multiply by -2 so you get....

    2x + 3y= 6

    -2(x - 2y= 10)

    (distribute)

    2x + 3y = 6

    -2x + 4y = -20

    ------------------------- (add together)

    0x + 7y = -14 (divide by 7)

    y = -2

    Then you can go back and use the same idea to solve for x by eliminating the ys.

    Good luck I hope this helps you!

  • 1 decade ago

    Graphing is kind of hard on a text interface, so I will skip that one. Graph the two lines and determine the x and y co-ordinates of the point of intersection, if any.

    In the substitution method, solve for one variable in one equation and SUBSTITUTE that expression into the other equation. Solve for each variable.

    In the addition method (also known as the elimination or subtraction method), multiply all terms in each equation so that one of the variables will add to 0.

    Substitution:

    I will solve for x in the second equation.

    x = 10 + 2y

    Sub into the first equation.

    2(10 +2y) + 3y = 6

    20 + 4y + 3y = 6

    7y = 6 - 20

    7y = -14

    y = -2

    Sub into the x = line above.

    x = 10 + 2y = 10 + 2(-2) = 10 - 4 = 6

    So x =6 and y = -2

    Addition method:

    2x+3y=6 Multiply by 2

    x-2y=10 Multiply by 3

    -----------------

    4x + 6y = 12

    3x - 6y = 30

    ------------------- Add these together

    7x + 0y = 42

    7x = 42

    x = 6

    Pick one of the original equations, sub in and solve. I choose the second sequation.

    6 - 2y = 10

    -2y = 10 - 6

    -2y = 4

    y = -2

    So x =6 and y = -2, which thankfully is the same answer as before.

  • 1 decade ago

    oh well...

    2x + 3y = 6

    x - 2y = 10

    find x or y first, in this case.:

    x = 10 + 2y

    then substitute it to x in the first equation:

    2(10 + 2y) + 3y = 6

    20 + 4y + 3y = 6

    20 + 7y = 6

    7y = 6 - 20

    7y = -14

    y = -14 / 7

    y = -2

    then substitute the value of y to the equation to get x, thus:

    x = 10 + 2(-2)

    = 10 - 4

    x = 6

    to check:

    2x + 3y = 6

    2(6) + 3(-2) = 6

    12 - 6 = 6

    6 = 6

    or

    x - 2y = 10

    6 - 2(-2) = 10

    6 - (-4) = 10

    6 + 4 = 10

    10 = 10

    just plot the points in a graph of x and y axes!

  • 1 decade ago

    Oh gosh.. I hated math, but I liked this. lol

    You need to get the "x" and then the "y" (or the other way around... however you'd like).

    2x + 3y = 6

    2x = -3y + 6

    x = -3/2y + 3

    If you don't want fractions then that would be x= -1.5y + 3

    x-2y=10

    x=2y + 10

    2y + 10 = -1.5y + 3

    Move the -1.5y over to the left (which would make it 1.5y) and the "+10" over to the right which would make the "+10" and "-10".

    3.5y - 7

    Then divide -7 into 3.5

    y= -2

    Then, you substitute "-2" for "y"

    x - 2(-2) = 10

    x + 4=10

    Move the 4 to the right would make it "-4"

    x=6

    You can check this easily to make sure you have the right answer:

    2(6) + 3 (-2) = 12-6 =6

    It'll be kind of hard to explain how to graph over the computer, but just make sure that your point of intersection is (-2,6). If it is, you most likely did it right. =)

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  • gladon
    Lv 4
    3 years ago

    i can not answer that, because of the fact for that fraction, i do no longer comprehend if the numerator is 5, (4+5), (2*4+5). comparable with the denominator. although, if i assume which you advise: 2 x 4 + (5 / 2) - 3 x 4 + 3 = then shop on with the order of operations, PEMDAS. That stands for Parentheses, Exponents, Multiplication, branch, Addition Subtraction. Multiplication and branch are executed on the comparable time yet from left to suitable, as are addition and subtraction. So first, you are able to not do something with what's in parentheses, and there are not any exponents, so start up with multiplication and branch: (2*4) + (5/2) -(3*4) +3 = 8 + (5/2) -12 +3 Now, upload or subtract from left to suitable: (8 5/2) -9 convert to incorrect fractions with a denominator of two: 21/2 - 18/2=3/2 So the respond is 3/2.

  • mom
    Lv 7
    1 decade ago

    You are asking a lot

    Solve this equation by graphing, substitution, and the addition method, and show work.

    2x+3y=6

    x-2y=10

    first substitution

    x=2y+10

    2(2y+10) +3y=6

    4y+20+3y=6

    7y=-14

    y=-2

    x=-4+10=6

    -----------------------------------

    add/sub

    Solve this equation by graphing, substitution, and the addition method, and show work.

    2x+3y=6

    x-2y=10 multiply this one by -2

    -2x+4y=-20 add to first one

    7y=-14

    y=-2

    x=6

    -------------------------------

    now the graphing

    Solve this equation by graphing, substitution, and the addition method, and show work.

    2x+3y=6 let x=0 so y=2 now let y=0 and x=3 plot these and draw a line.

    x-2y=10 same here. Let x=0, y=-5 then y=0, x=10. Plot and draw line. the point of intersection should be (6,-2)

  • 1 decade ago

    ( 2 x) x-2y=10

    2x - 4y = 20

    2x+ 3y = 6

    subtract

    -7y = 14

    y = - 2

    substitute into x-2y=10

    x + 4 = 10

    x= 10-4 = 6

    x= 6

    check 2(6) + 3( -2) = 12-6 =6

  • 1 decade ago

    substitution

    2x+3y=6

    2x=6-3y

    x=3- 1.5y

    x-2y=10

    x=10+2y

    10+2y= 3 - 1.5y

    3.5y=-7

    y=-2

    PLUG IN y=-2

    x - (2x-2)=10

    x+4=10

    x=6

    Source(s): best answer plz
  • 1 decade ago

    ok here:

    2x+3y=6

    x-2y=10

    +2y +2y

    x=2y+10

    2(2y+10)+3y=6

    4y+20+3y=6

    -20 -20

    4y=-14

    y=7/2

    now plug it in for y

    x-2(7/2)=10

    x-7=10

    +7 +7

    x=17

    so

    (17,7/2)

  • 1 decade ago

    2x+3y=6 -2(x-2y= 10 )try to get the x's to cancel and solve for y. so it would look like this 2x+3y=6 ..................................-2x+4y=-20 cancel the x's to get ........................................7y=-14 then divide by 7 to get y=-2 substitute it back in to find x and you get x=6 ordered pair is (6,-2)

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