I need help with substitution! Find the solution. Here are the two equations: 5x – 6y =19 4x + 3y = 10

Question

I need help with substitution! Find the solution.
Here are the two equations:
5x – 6y =19
4x + 3y = 10

0

Answers ( No )

    0
    2021-10-14T01:26:44+00:00

    Solve the following system using substitution:
    {5 x – 6 y = 19
    {4 x + 3 y = 10

    In the first equation, look to solve for x:
    {5 x – 6 y = 19
    {4 x + 3 y = 10

    Add 6 y to both sides:
    {5 x = 6 y + 19
    {4 x + 3 y = 10

    Divide both sides by 5:
    {x = (6 y)/5 + 19/5
    {4 x + 3 y = 10

    Substitute x = (6 y)/5 + 19/5 into the second equation:
    {x = (6 y)/5 + 19/5
    {3 y + 4 ((6 y)/5 + 19/5) = 10

    3 y + 4 ((6 y)/5 + 19/5) = ((24 y)/5 + 76/5) + 3 y = (39 y)/5 + 76/5:
    {x = (6 y)/5 + 19/5
    {(39 y)/5 + 76/5 = 10

    In the second equation, look to solve for y:
    {x = (6 y)/5 + 19/5
    {(39 y)/5 + 76/5 = 10

    Subtract 76/5 from both sides:
    {x = (6 y)/5 + 19/5
    {(39 y)/5 = -26/5

    Multiply both sides by 5/39:
    {x = (6 y)/5 + 19/5
    {y = -2/3

    Substitute y = -2/3 into the first equation:

    Answer:  {x = 3, y = -2/3

    0
    2021-10-14T01:27:07+00:00

    5x – 6y = 19 ————- (1)
    4x + 3y = 10 ————-(2)

    From (2):
    4x + 3y = 10
    3y = 10 – 4x
    6y = 20 – 8x ——– sub into (1)

    5x – (20 – 8x) = 19
    5x – 20 + 8x = 19
    13x – 20 = 19
    13x = 19 + 20
    13x = 39
    x = 3 —- sub into (1)
    5 (3) – 6y = 19
    -6y = 19 – 15
    -6y = 4
    y = – 2/3

    Ans: x = 3, y = -2/3

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