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Sagot :
Notice that the coefficient of the variable y in the first equation is +3 and in the second equation is -3. Then, if we add both equations together, they will cancel out.
Add both equations (left member pus left member equals right member plus right member):
[tex]\begin{gathered} -10x+3y=2 \\ x-3y=16 \\ \Rightarrow(-10x+3y)+(x-3y)=2+16 \\ \Rightarrow-10x+3y+x-3y=18 \\ \Rightarrow-10x+x+3y-3y=18 \\ \Rightarrow-9x=18 \end{gathered}[/tex]Notice that we got an equation that just involves the variable x. Solve for x:
[tex]\begin{gathered} \Rightarrow x=\frac{18}{-9} \\ \Rightarrow x=-2 \end{gathered}[/tex]Replace x=-2 into one of the equations to find the value of y:
[tex]\begin{gathered} -10x+3y=2 \\ \Rightarrow-10(-2)+3y=2 \\ \Rightarrow20+3y=2 \\ \Rightarrow3y=2-20 \\ \Rightarrow3y=-18 \\ \Rightarrow y=-\frac{18}{3} \\ \Rightarrow y=-6 \end{gathered}[/tex]Therefore, the solution for this system of equations, is:
x = -2 ; y = -6
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