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x - y = -2
4x - y = 4

Sagot :

VectorFundament120idn

Explanation

  • Given the system of equations.

[tex] \begin{cases} x - y = - 2 \\ 4x - y = 4 \end{cases}[/tex]

  • Use the elimination method as it is faster. We have to eliminate the y-term. (You can eliminate the x-term but it takes longer than eliminating y-term.)

Simply multiply the negative one in one of the equations.

[tex] \begin{cases} - x + y = 2 \\ 4x - y = 4 \end{cases}[/tex]

We can finally eliminate the y-term by adding both equations.

[tex]( - x + 4x) + (y - y) = 2 + 4 \\ 3x + 0 = 6 \\ 3x = 6 \\ x = \frac{ 6 }{3} \longrightarrow \frac{ \cancel{6}}{ \cancel{3}} = 2 \\ x = 2[/tex]

  • Substitute the value of x in any given equations. I will substitute in the first equation.

[tex]x - y = - 2 \\ 2 - y = - 2 \\ 2 + 2 = y \\ 4 = y[/tex]

  • Check the answer by substituting the value of x and y in both equations.

First Equation

[tex]x - y = - 2 \\ 2 - 4 = - 2 \\ - 2 = - 2 \longrightarrow \sf{true} \: \: \green{ \checkmark}[/tex]

Second Equation

[tex]4x - y = 4 \\ 4(2) - 4 = 4 \\ 8 - 4 = 4 \\ 4 = 4 \longrightarrow \sf{true} \: \: \green{ \checkmark}[/tex]

Hence, the solution is (2,4).

Answer

[tex] \begin{cases} x = 2 \\ y = 4 \end{cases}[/tex]

Coordinate Form

[tex](2,4)[/tex]

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