Q. 4.16 Solve the system by substitution... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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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91影视

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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91影视

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

Mechanics Maths

Decision Maths

Applied Mathematics

Pure Maths

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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