Question

4.

(08.05)

Which of the following ordered pairs represents the solution to the system given below? (4 points)

2x + y = 20
4x − 2y = 40

(10, 0)
(0, 10)
(4, 2)
(10, −10)

Answer 1

`$(10, 0)$`

Explanation:

Let's try all the options:

`$\left \{ {{2x + y = 20} \atop {4x-2y = 40} \right. $`

Considering
`$(10, 0)$`:

`$\left \{ {{2(10) + 0 = 20} \atop {4(10)-2(0) = 40} \right. $\\`

`$\left \{ {{20 + 0 = 20} \atop {40-0 = 40} \right. $`

`$\left \{ {{20= 20} \atop {40 = 40} \right. $`

Considering
`$(0, 10)$`:

`$\left \{ {{2(0) + 10 = 20} \atop {4(0)-2(10) = 40} \right. $\\`

`$\left \{ {{0 + 10 = 20} \atop {0-20 = 40} \right. $`

`$\left \{ {{10= 20} \atop {-20 = 40} \right. $`

`$\left \{ {{10\\eq 20} \atop {-20 \\eq 40} \right. $`

Considering
`$(4, 2)$`:

`$\left \{ {{2(4) + 2 = 20} \atop {4(4)-2(2) = 40} \right. $\\`

`$\left \{ {{8 + 2 = 20} \atop {8-4 = 40} \right. $`

`$\left \{ {{10= 20} \atop {4 = 40} \right. $`

`$\left \{ {{10\\eq 20} \atop {4 \\eq 40} \right. $`

Considering
`$(10, -10)$`:

`$\left \{ {{2(10) -10 = 20} \atop {4(10)-2(-10) = 40} \right. $\\`

`$\left \{ {{20 -10 = 20} \atop {40+20 = 40} \right. $`

`$\left \{ {{10= 20} \atop {60 = 40} \right. $`

`$\left \{ {{10\\eq 20} \atop {60 \\eq 40} \right. $`