Chapter 4: Q. 372 (page 481)

Solve the system of equations.
$\{\begin{cases} 5 x + 3 y = - 6 \\ 2 y + 3 z = - 1 \\ 7 x + z = 1 \end{cases}$

Short Answer

Expert verified

The solution for the system of equations is,

$x = 0 y = - 2 z = 1$ .

Step by step solution

Step 1. Given the information.

The system of equations is,

$\{\begin{cases} 5 x + 3 y = - 6 . . . . . . . . . . . (1) \\ 2 y + 3 z = - 1 . . . . . . . . . . . (2) \\ 7 x + z = 1 . . . . . . . . . . . . . . . . (3) \end{cases}$

Step 2. Eliminating z from equations (2) and (3).

Eliminating $z$ from equations (2) and (3).

$2 y + 3 z = - 1 . . . . . . . . . (2) - 21 x - 3 z = - 3 . . . . (3) \times - 3$

Solving the equations, we get,

$- 21 x + 2 y = - 4 . . . . . . . . . (4)$

Step 3. Finding the value of x.

Solving equation (1) and (4)

$10 x + 6 y = - 12 . . . . . . . . (1) \times 2 - 63 x + 6 y = - 12 . . . . . (2) \times 3$

Subtracting the equations, we get,

$73 x = 0 x = 0$

Step 4. Finding the value of y.

Substituting $x = 0$ in the equation

$5 x + 3 y = - 6$ ,

$5 (0) + 3 y = - 6 0 + 3 y = - 6 3 y = - 6 y = - 2$

Step 5. Finding the value of z.

Substituting $x = 0$ in the equation

$7 x + z = 1$ ,

$7 (0) + z = 1 0 + z = 1 z = 1$

Step 6. Checking the solution for the equation 5x+3y=-6.

Substituting $x = 0 y = - 2$ in the equation

$5 x + 3 y = - 6$ ,

$5 (0) + 3 (- 2) = - 6 0 - 6 = - 6 - 6 = - 6$

This is true.

Step 7. Checking the solution for the equation 2y+3z=-1

Substituting $y = - 2 z = 1$ in the equation

$2 y + 3 z = - 1$ ,

$2 (- 2) + 3 (1) = - 1 - 4 + 3 = - 1 - 1 = - 1$

This is true.

Step 8. Checking the solution for the equation 7x+z=1.

Substituting $x = 0 z = 1$ in the equation

$7 x + z = 1$ ,

$7 (0) + 1 = 1 0 + 1 = 1 1 = 1$

This is true.

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Solve the system of equations.
$\{\begin{cases} 5 x + 3 y = - 6 \\ 2 y + 3 z = - 1 \\ 7 x + z = 1 \end{cases}$

Short Answer

Step by step solution

Step 1. Given the information.

Step 2. Eliminating z from equations (2) and (3).

Step 3. Finding the value of x.

Step 4. Finding the value of y.

Step 5. Finding the value of z.

Step 6. Checking the solution for the equation 5x+3y=-6.

Step 7. Checking the solution for the equation 2y+3z=-1

Step 8. Checking the solution for the equation 7x+z=1.

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Solve the system of equations.5x+3y=-62y+3z=-17x+z=1

Short Answer

Step by step solution

Step 1. Given the information.

Step 2. Eliminating z from equations (2) and (3).

Step 3. Finding the value of x.

Step 4. Finding the value of y.

Step 5. Finding the value of z.

Step 6. Checking the solution for the equation 5x+3y=-6.

Step 7. Checking the solution for the equation 2y+3z=-1

Step 8. Checking the solution for the equation 7x+z=1.

One App. One Place for Learning.

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Solve the system of equations.
$\{\begin{cases} 5 x + 3 y = - 6 \\ 2 y + 3 z = - 1 \\ 7 x + z = 1 \end{cases}$