Solve the following systems using the elimination method.


  1. Answer:
    The end result of this exercise is x = 1, y = 1.
    Step-by-step explanation:
    To solve by elimination, the coefficients of one of the variables must coincide in the two equations, so that the variable vanishes when one equation is subtracted from the other.
    • 5x−y=4,4x+y=5
    To make 5x and 4x equal, multiply all the terms on each side of the first equation by 4 and all the terms on each side of the second by 5.
    • 4×5x+4(−1)y=4×4, 5×4x+5y=5×5
    • 20x−4y=16, 20x+5y=25
    Subtract 20x+5y=25 from 20x−4y=16. To do this, subtract like terms on both sides of the equals sign.
    • 20x−20x−4y−5y=16−25
    Add 20x and −20x. Terms 20x and −20x cancel, leaving a single-variable equation that can be solved.
    • −4y−5y=16−25
    Add −4y and −5y.
    • −9y=16−25
    Add 16 and −25.
    • −9y=−9
    Divide both sides by −9.
    • y = 1 =====> First result
    Substitute 1 for y in 4x+y=5. Since the resulting equation only contains one variable, it can be solved for x directly.
    • 4x+1=5
    Subtract 1 from both sides of the equation.
    • 4x=4
    Divide both sides by 4.
    • x = 1 =====> Second result.

  2. Answer:
    x=1, y=1  
    Step-by-step explanation:
    You need to plug the two equations together. This means that you can do the addition method because y and -y have the same abosute value but they have differnet signs. So you add 5x-y=4 and 4x+y=5 thats going to be 9x+0=9 (9x=9) and you have to divide 9 to both sides. You do that and you get x=1. Then you have to solve for y. You just plug it in any equation. Lets do 4x+y=5. When you plug x in it it will be 4(1)+y=5. You simplify it and it will be 4+y=5 subtract 4 to both sides to get y=1 and you are done.


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