Question

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Given the equations 2x-3y=-6 and x+3y+-12, solve for x and y by substitution, elimination, and graphing.

Answers

  1. The solution of the set of equation 2x-3y=-6 and x+3y+-12 is (-6,-2).

    What is Substitution, Elimination and Graphing methord of solving Equation?

    By Substitution Method:
    1. Resolve ONE of the x or y equations. If one of the equations has previously been solved for x or y, this step can be avoided.
    2. Substitute the outcome for that variable in the other equation.
    3. Either all x terms or all y terms will now make up the new equation. Fix the variable’s place in the equation.
    4. To obtain the alternative answer, plug the solution back into the beginning equation (the one you used to solve for x or y).
    When using the Elimination method,
    start by aligning the x- and y-coordinates on the same side of the equation.
    2. Whichever you decide to remove, find a common multiple for the Xs OR the Ys.
    3. To enable the addition of the equations, make one of those multiples negative.
    4. One of the variables will be removed when the equations are combined. Give the variable that is still present its final solution.
    5. To determine the other number, enter your response from step four into either of the equations.
    Graphing a solution:
    1. Rewrite the initial y equation in the form y = mx + b a. Step 2 can be immediately followed if the line has previously been solved for y.
    2. Draw a line to represent the first equation.
    3. Apply the second equation to steps 1 and 2 as before.
    4. The intersection of the two lines represents the system’s solution. There are infinitely many solutions if the lines match. There are no solutions if the lines are parallel and do not intersect.
    Substitution methord,
    The equations are
    2x -3y = -6
    ⇒ x  = 3/2y – 3.
    Putting this value in the second equation we get,
    (3/2)y – 3 + 3y = -12
    ⇒(9/2)y = -9
    ⇒y = -2.
    Therefore,
    x = (3/2)y – 3 = (3/2)(-2) – 3 = -6
    x = -6, y = -2.
    By Elimination Methord ,
    2x- 3y = -6
    x + 3y =-12
    simply adding both equation we get,
    3x = -18
    x = -6.
    and y = -2
    For graphical methord plot both lines in the graph then find the point where they intersect it will be (-6,-2).
    To learn more about System of Linear equation refer to :
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