Answer:
[tex]$(10, 0)$[/tex]
Step-by-step explanation:
Let's try all the options:
[tex]$\left \{ {{2x + y = 20} \atop {4x-2y = 40} \right. $[/tex]
Considering [tex]$(10, 0)$[/tex]:
[tex]$\left \{ {{2(10) + 0 = 20} \atop {4(10)-2(0) = 40} \right. $\\[/tex]
[tex]$\left \{ {{20 + 0 = 20} \atop {40-0 = 40} \right. $[/tex]
[tex]$\left \{ {{20= 20} \atop {40 = 40} \right. $[/tex]
Considering [tex]$(0, 10)$[/tex]:
[tex]$\left \{ {{2(0) + 10 = 20} \atop {4(0)-2(10) = 40} \right. $\\[/tex]
[tex]$\left \{ {{0 + 10 = 20} \atop {0-20 = 40} \right. $[/tex]
[tex]$\left \{ {{10= 20} \atop {-20 = 40} \right. $[/tex]
[tex]$\left \{ {{10\neq 20} \atop {-20 \neq 40} \right. $[/tex]
Considering [tex]$(4, 2)$[/tex]:
[tex]$\left \{ {{2(4) + 2 = 20} \atop {4(4)-2(2) = 40} \right. $\\[/tex]
[tex]$\left \{ {{8 + 2 = 20} \atop {8-4 = 40} \right. $[/tex]
[tex]$\left \{ {{10= 20} \atop {4 = 40} \right. $[/tex]
[tex]$\left \{ {{10\neq 20} \atop {4 \neq 40} \right. $[/tex]
Considering [tex]$(10, -10)$[/tex]:
[tex]$\left \{ {{2(10) -10 = 20} \atop {4(10)-2(-10) = 40} \right. $\\[/tex]
[tex]$\left \{ {{20 -10 = 20} \atop {40+20 = 40} \right. $[/tex]
[tex]$\left \{ {{10= 20} \atop {60 = 40} \right. $[/tex]
[tex]$\left \{ {{10\neq 20} \atop {60 \neq 40} \right. $[/tex]
