Chapter 4: Q. 409 (page 485)

In the following exercises, solve each system of equations. Use either substitution or elimination.
$\{\begin{cases} x + 4 y = 6 \\ - 2 x + y = - 3 \end{cases}$

Short Answer

Expert verified

The solution for the system of the equation $\{\begin{cases} x + 4 y = 6 \\ - 2 x + y = - 3 \end{cases}$ is $(2, 1)$

Step by step solution

Step 1. Given

The system of equations $\{\begin{cases} x + 4 y = 6 \\ - 2 x + y = - 3 \end{cases}$

To find the solution of the system of equations.

Step 2. Solve the equations

Consider the system of equations:

$x + 4 y = 6$

$- 2 x + y = - 3$

Solve the first equation for $x$ ,

$x = 6 - 4 y$

Step 3. Solve for y

Substitute $x = 6 - 4 y$ in the second equation,

$- 2 (6 - 4 y) + y = - 3$

$- 12 + 8 y + y = - 3$

$9 y = 9$

Divide both sides of the equation by $9$ ,

$y = 1$

Step 4. Solve for x

Substitute $y = 1$ in the first equation,

$x + 4 y = 6$

$x + 4 (1) = 6$

$x = 6 - 4$

$x = 2$

The solution of the equation is $(2, 1)$

Step 5. Check the solution

Substitute $(2, 1)$ in both the equations,

$x + 4 y = 6$

$2 + 4 (1) = 6$

$6 = 6$ is true.

Then $- 2 x + y = - 3$

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

$- 3 = - 3$ is true.

Hence the solution has been checked.

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In the following exercises, solve each system of equations. Use either substitution or elimination.
$\{\begin{cases} x + 4 y = 6 \\ - 2 x + y = - 3 \end{cases}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Solve the equations

Step 3. Solve for y

Step 4. Solve for x

Step 5. Check the solution

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In the following exercises, solve each system of equations. Use either substitution or elimination.x+4y=6-2x+y=-3

Short Answer

Step by step solution

Step 1. Given

Step 2. Solve the equations

Step 3. Solve for y

Step 4. Solve for x

Step 5. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system of equations. Use either substitution or elimination.
$\{\begin{cases} x + 4 y = 6 \\ - 2 x + y = - 3 \end{cases}$