Answer:
Set a system of equations:
[tex]\left \{ {{2x+8y=3} \atop {4x-3y=2}} \right.[/tex]
Multiply the whole upper equation by 2 and the whole bottom equation by 1 so their x-value equals:
[tex]\left \{ {{2(2)x+8(2)y=3(2)} \atop {4(1)x-3(1)y=2(1)}} \right.\\\\=\left \{ {{4x+16y=6} \atop {4x-3y=2}} \right.[/tex]
Subtract the upper equation by the bottom equation & solve for y:
[tex](4x-4x)+(16y-(-3y))=6-2\\\\19y=4\\\\y=\frac{4}{19}[/tex]
Substitute in the y-value to a equation to find x:
[tex]2x+8y=3\\\\2x+8(\frac{4}{19} )=3\\\\2x=3-\frac{32}{19} =\frac{57}{19} -\frac{32}{19} =\frac{25}{19} \\\\x=\frac{\frac{25}{19}}{2} =\frac{25}{19}*\frac{1}{2} =\frac{25}{38}[/tex]
Therefore, the answer would be:
[tex]\left \{ {{y=\frac{4}{19} } \atop {x=\frac{25}{38} }} \right.[/tex]
