Answer by using elimination?

2x+5y=2

3x-2y=3

4 Answers

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  • Anonymous
    1 decade ago
    Favorite Answer

    There's 2 ways to solve a system of equations: substitution (solving for 1 variable and plugging it into the other equation) or elimination. In using the elimination method we come up with a way to add or subtract the equations to eliminate a variable. In this case we have to multiply each equation by something in order to get it to "eliminate."

    If I multiply the first one by 3 and the second by -2, when I combine the two equations I will have eliminated the x's and just have y's.

    3(2x+5y=2)

    6x+15y=6

    and

    -2(3x-2y=3)

    -6x+4y=-6

    Combine:

    6x+15y=6

    -6x+4y=-6

    _____________

    19y=0

    y=0

    Similarly, multiply the first by 2 and second by 5 to eliminate the y's.

    2(2x+5y=2)

    4x+10y=4

    and

    5(3x-2y=3)

    15x-10y=15

    Combine:

    4x+10y=4

    15x-10y=15

    _____________

    19x=19

    x=1

    And just for fun, we can check it ;)

    x=1, y=0

    2(1)+5(0)=2

    2+0=2

    2=2 check :)

    3(1)-2(0)=3

    3-0+3

    3=3 check :)

  • Anonymous
    1 decade ago

    You've got 5y in the first and -2y in the second, so multiply the first equation by 2/5 and add it to the second. This gives you

    (2/5)2x + 2y + 3x - 2y = 2(2/5) + 3

    (2/5)2x + 3x = 2(2/5) + 3

    2*2x + 15x = 2(2) + 15

    19x = 19

    x = 1

    Now you can plug this in and solve for y.

  • 1 decade ago

    2x+5y=2 (1)

    3x-2y=3 (2)

    2 x (1) gives 4x +10y = 4 (3)

    5 x (2) gives 15x -10y = 15 (4)

    (3) + (4) gives 19x = 19

    x = 1

    Sub. x=1 into (1)

    2 + 5y = 2

    5y = 0

    y = 0

    Answer: ( 1,0)

  • 1 decade ago

    Elimination of X or Y?

    if you eliminate one you can easily find the other!

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