Chapter 4: Q. 4.15 (page 378)

Solve the system by substitution: $\{\begin{cases} x - 4 y = - 4 \\ - 3 x + 4 y = 0 \end{cases}$

Short Answer

Expert verified

The solution of the system of equations is $(2, \frac{3}{2})$ .

Step by step solution

Step 1. Given Information.

The system of equations is:

$\{\begin{cases} x - 4 y = - 4 \\ - 3 x + 4 y = 0 \end{cases}$

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

We'll solve for the second equation for $y$ ,

$- 3 x + 4 y = 0$

$4 y = 3 x$

$y = \frac{3}{4} x$

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

Replace the $y$ with $\frac{3}{4} x$ ,

$x - 4 y = - 4$

$x - 4 (\frac{3}{4} x) = - 4$

Step 4. Solve the resulting equation.

Now we have an equation with just one variable.

$x - 4 (\frac{3}{4} x) = - 4$

$x - 3 x = - 4$

$2 x = 4$

$x = 2$

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

We'll use the second equation and replace $x$ with 2.

- 3 x + 4 y = 0

$- 3 (2) + 4 y = 0$

$4 y = 6$

$y = \frac{3}{2}$

Step 6. Write the solution as an ordered pair.

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

$(2, \frac{3}{2})$

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

Substitute $x, y = 2, \frac{3}{2}$ into both equations and make sure they are both true.

$x - 4 y = - 4$

$2 - 4 (\frac{3}{2}) = - 4$

$2 - 6 = - 4$

$- 4 = - 4$

And,

- 3 x + 4 y = 0

$- 3 (2) + 4 (\frac{3}{2}) = 0$

$- 6 + 6 = 0$

$0 = 0$

Both equations are True.

The point $(2, \frac{3}{2})$ is the solution to the system.

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Solve the system by substitution: $\{\begin{cases} x - 4 y = - 4 \\ - 3 x + 4 y = 0 \end{cases}$

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:x-4y=-4-3x+4y=0

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

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Solve the system by substitution: $\{\begin{cases} x - 4 y = - 4 \\ - 3 x + 4 y = 0 \end{cases}$