Diketahui sistem persamaan 2x − y = 4, 2x + 3z = 14, dan 2y − z + 8 = 0. Berdasarkan sistem persamaan…

Question

Diketahui sistem persamaan 2x − y = 4, 2x + 3z = 14, dan 2y − z + 8 = 0. Berdasarkan sistem persamaan tersebut, persamaan berikut yang bernilai paling besar adalah ...

ScanSolve AI Tutor · Accepted Answer

To find the expression with the largest value, we first need to solve the given system of linear equations for $x$ , $y$ , and $z$ .

The system of equations is:

$2x - y = 4$
$2x + 3z = 14$
$2y - z + 8 = 0 \implies 2y - z = -8$

Express $y$ in terms of $x$ from equation (1).
From $2x - y = 4$ , we get $y = 2x - 4$ . (Equation 1a)
Express $z$ in terms of $y$ from equation (3).
From $2y - z = -8$ , we get $z = 2y + 8$ . (Equation 3a)
Substitute Equation 1a into Equation 3a to express $z$ in terms of $x$ .
$z = 2(2x - 4) + 8$ $z = 4x - 8 + 8$
$z = 4x$ (Equation 3b)
Substitute Equation 3b into equation (2) to solve for $x$ .
$2x + 3(4x) = 14$ $2x + 12x = 14$ $14x = 14$ $x = 1$
Substitute the value of $x$ back into Equation 1a and Equation 3b to find $y$ and $z$ .
For $y$ :
$y = 2(1) - 4$ $y = 2 - 4$ $y = -2$
For $z$ :
$z = 4(1)$ $z = 4$
So, the solution to the system is $x=1$ , $y=-2$ , $z=4$ .
Evaluate each given expression using $x=1$ , $y=-2$ , and $z=4$ .
A. $x + 2y = 1 + 2(-2) = 1 - 4 = -3$
B. $2y + z = 2(-2) + 4 = -4 + 4 = 0$
C. $2x - 3z = 2(1) - 3(4) = 2 - 12 = -10$
D. $3y + z = 3(-2) + 4 = -6 + 4 = -2$
E. $3x - z = 3(1) - 4 = 3 - 4 = -1$
Compare the values to find the largest one.
The values are -3, 0, -10, -2, and -1. The largest value among these is 0.

The expression with the largest value is $2y + z$ .

The final answer is $\boxed{\text{B. } 2y + z}$ .

Diketahui sistem persamaan 2x − y = 4, 2x + 3z = 14, dan 2y − z + 8 = 0. Berdasarkan sistem persamaan tersebut, persamaan berikut yang bernilai paling besar adalah ...

Step-by-step solution

Express $y$ in terms of $x$ from equation (1).

Express $z$ in terms of $y$ from equation (3).

Substitute Equation 1a into Equation 3a to express $z$ in terms of $x$ .

Substitute Equation 3b into equation (2) to solve for $x$ .

Substitute the value of $x$ back into Equation 1a and Equation 3b to find $y$ and $z$ .

Evaluate each given expression using $x=1$ , $y=-2$ , and $z=4$ .

Compare the values to find the largest one.

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More Mathematics Questions

Diketahui sistem persamaan 2x − y = 4, 2x + 3z = 14, dan 2y − z + 8 = 0. Berdasarkan sistem persamaan tersebut, persamaan berikut yang bernilai paling besar adalah ...

Step-by-step solution

Express yyy in terms of xxx from equation (1).

Express zzz in terms of yyy from equation (3).

Substitute Equation 1a into Equation 3a to express zzz in terms of xxx.

Substitute Equation 3b into equation (2) to solve for xxx.

Substitute the value of xxx back into Equation 1a and Equation 3b to find yyy and zzz.

Evaluate each given expression using x=1x=1x=1, y=−2y=-2y=−2, and z=4z=4z=4.

Compare the values to find the largest one.

Still stuck on this one?

More Mathematics Questions

Express $y$ in terms of $x$ from equation (1).

Express $z$ in terms of $y$ from equation (3).

Substitute Equation 1a into Equation 3a to express $z$ in terms of $x$ .

Substitute Equation 3b into equation (2) to solve for $x$ .

Substitute the value of $x$ back into Equation 1a and Equation 3b to find $y$ and $z$ .

Evaluate each given expression using $x=1$ , $y=-2$ , and $z=4$ .