Chapter 4: Q. 4.13 (page 377)

Solve the system by substitution: $\{\begin{cases} - 2 x + y = - 11 \\ x + 3 y = 9 \end{cases}$

Short Answer

Expert verified

Solution of the system of equations is $(6, 1)$ .

Step by step solution

Step 1. Given Information.

System of equations is $\{\begin{cases} - 2 x + y = - 11 \\ x + 3 y = 9 \end{cases}$

Step 2. Solve one of the equations for either variable.

We'll solve for the first equation for y.

- 2 x + y = - 11

$y = 2 x - 11$

Step 3. Substitute the expression from Step 2 into the other equation.

We replace $y$ in the second equation with the expression $2 x - 11$ .

$x + 3 y = 9$

$x + 3 (2 x - 11) = 9$

Step 4. Solve the resulting equation.

Now we have an equation with just one variable.

$x + 3 (2 x - 11) = 9$

$x + 6 x - 33 = 9$

$7 x = 42$

$x = 6$

Step 5. Substitute the solution from Step 4 into one of the original equations to find the other variable.

We'll use the first equation and replace $x$ with 6.

- 2 x + y = - 11

$- 2 (6) + y = - 11$

$- 12 + y = - 11$

$y = 1$

Step 6. Write the solution as an ordered pair.

The ordered pair is $(x, y) .$

$(6, 1)$

Step 7. Check that the ordered pair is a solution to both original equations.

Substitute $x, y = 6, 1$ into both equations and make sure they are both true.

$- 2 x + y = - 11$

$- 2 (6) + 1 = - 11$

$- 11 = - 11$

And, $x + 3 y = 9$

$6 + 3 (1) = 9$

$9 = 9$

Both equations are True.

$(6, 1)$ is the solution to the system.

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Solve the system by substitution: $\{\begin{cases} - 2 x + y = - 11 \\ x + 3 y = 9 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve one of the equations for either variable.

Step 3. Substitute the expression from Step 2 into the other equation.

Step 4. Solve the resulting equation.

Step 5. Substitute the solution from Step 4 into one of the original equations to find the other variable.

Step 6. Write the solution as an ordered pair.

Step 7. Check that the ordered pair is a solution to both original equations.

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Solve the system by substitution:-2x+y=-11x+3y=9

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve one of the equations for either variable.

Step 3. Substitute the expression from Step 2 into the other equation.

Step 4. Solve the resulting equation.

Step 5. Substitute the solution from Step 4 into one of the original equations to find the other variable.

Step 6. Write the solution as an ordered pair.

Step 7. Check that the ordered pair is a solution to both original equations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Pure Maths

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the system by substitution: $\{\begin{cases} - 2 x + y = - 11 \\ x + 3 y = 9 \end{cases}$