System of Linear Equations - Elimination 2

Algebra Level 1

Solve the following system of equations: { 2 x + y = 7 4 x − y = 5. \begin{cases} 2x+y=7 \\ 4x-y=5. \end{cases}

x = 1 , y = 5 x = 1, y = 5 x = 2 , y = 3 x = 2, y = 3 x = 3 , y = 7 x = 3, y = 7 x = 3 , y = 1 x = 3, y = 1

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2 solutions

Lucas Tu
Sep 4, 2020

if you added the 2 equations together, you get 6 x x = 12 then it is easy to work out that x x is 2. the only option in which x x is 2 in the second one.

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Brilliant Mathematics Staff
Aug 1, 2020

We are given the following two linear equations:

{ 2 x + y = 7 ( 1 ) 4 x − y = 5. ( 2 ) \begin{cases} 2x+y=7 &\qquad (1) \\ 4x-y=5. &\qquad (2) \end{cases}

Taking ( 1 ) + ( 2 ) (1)+(2) gives 6 x = 12 , 6x=12, or x = 2. x=2.
Substituting x = 2 x=2 into ( 1 ) (1) gives y = 3. y=3.
Therefore, the solution to the given system of linear equations is x = 2 , y = 3. x=2, y=3.

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