Chapter 4: Q. 4.16 (page 378)

Solve the system by substitution:
$\{\begin{cases} 4 x - y = 0 \\ 2 x - 3 y = 5 \end{cases}$

Short Answer

Expert verified

The solution of the system of equations is $(- \frac{1}{2}, - 2)$ .

Step by step solution

Step 1. Given Information.

System of equations is $\{\begin{cases} 4 x - y = 0 \\ 2 x - 3 y = 5 \end{cases}$ .

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

We'll solve for the first equation for y.

$\begin{array}{rcl} 4 x - y & = & 0 \\ y & = & 4 x \end{array}$

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

Replace the $y$ with $4 x$ ,

2 x - 3 y = 5

$2 x - 3 (4 x) = 5$

Step 4. Solve the resulting equation.

Now we have an equation with just one variable.

$\begin{array}{rcl} 2 x - 3 (4 x) & = & 5 \\ 2 x - 12 x & = & 5 \\ - 10 x & = & 5 \\ x & = & - \frac{1}{2} \end{array}$

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 $- \frac{1}{2}$ .

localid="1644477708322"

\begin{array}{rcl} 4 x - y & = & 0 \\ 4 (- \frac{1}{2}) - y & = & 0 \\ - 2 - y & = & 0 \\ y & = & - 2 \end{array}

Step 6. Write the solution as an ordered pair.

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

$(- \frac{1}{2}, - 2)$

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

Substitute $x, y = - \frac{1}{2}, - 2$ into both equations and make sure they are both true.

$4 x - y = 0$

$4 (- \frac{1}{2}) - (- 2) = 0$

$- 2 + 2 = 0$

$0 = 0$

And,

$2 x - 3 y = 5$

$2 (- \frac{1}{2}) - 3 (- 2) = 5$

$- 1 + 6 = 5$

$5 = 5$

Both equations are True.

The point $(- \frac{1}{2}, - 2)$ is the solution to the system.

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Solve the system by substitution:
$\{\begin{cases} 4 x - y = 0 \\ 2 x - 3 y = 5 \end{cases}$

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:4x-y=02x-3y=5

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

Logic and Functions

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Solve the system by substitution:
$\{\begin{cases} 4 x - y = 0 \\ 2 x - 3 y = 5 \end{cases}$