Chapter 4: Q. 4.20 (page 381)

Solve the system by elimination: $\{\begin{cases} 7 x + 8 y = 4 \\ 3 x - 5 y = 27 \end{cases}$

Short Answer

Expert verified

The solution of the system of equations is $(4, - 3)$ .

Step by step solution

Step 1. Given Information.

We have been given system of equations $\{\begin{cases} 7 x + 8 y = 4 \\ 3 x - 5 y = 27 \end{cases}$ .

Step 2. Eliminate the y's.

To get opposite coefficients of y, we will multiply the first equation by 5 and the second equation by 8.

$\{\begin{cases} 5 (7 x + 8 y) = 5 (4) \\ 8 (3 x - 5 y) = 8 (27) \end{cases}$

localid="1644381617193"

\{\begin{cases} 35 x + 40 y = 20 \\ 24 x - 40 y = 216 \end{cases}

Step 3. Add the equations resulting from Step 2 to eliminate one variable and solve it.

Add the $x' s, y' s$ and constants.

$\{\begin{cases} 35 x + 40 y = 20 \\ 24 x - 40 y = 216 \end{cases}$

59 x = 236

$x = 4$

Step 4. Substitute the solution from Step 3 into one of the original equation and solve for the other variable.

Substitute $x = 4$ into the first equation.

$7 x + 8 y = 4$

$7 (4) + 8 y = 4$

$28 + 8 y = 4$

$8 y = - 24$

$y = - 3$

Step 5. Write the solution as an ordered pair.

Write it as $(x, y)$ .

$(4, - 3)$

Step 6. Check that the ordered pair is a solution to both original equations.

Substitute $x, y = 4, - 3$ into both original equations.

$7 x + 8 y = 4$

$7 (4) + 8 (- 3) = 4$

$28 - 24 = 4$

$4 = 4$

And, $3 x - 5 y = 27$

$3 (4) - 5 (- 3) = 27$

$12 + 15 = 27$

$27 = 27$

Both equations are True.

The point

(4, - 3)

is the solution to the system.

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Solve the system by elimination: $\{\begin{cases} 7 x + 8 y = 4 \\ 3 x - 5 y = 27 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Eliminate the y's.

Step 3. Add the equations resulting from Step 2 to eliminate one variable and solve it.

Step 4. Substitute the solution from Step 3 into one of the original equation and solve for the other variable.

Step 5. Write the solution as an ordered pair.

Step 6. Check that the ordered pair is a solution to both original equations.

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Solve the system by elimination:7x+8y=43x-5y=27

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Eliminate the y's.

Step 3. Add the equations resulting from Step 2 to eliminate one variable and solve it.

Step 4. Substitute the solution from Step 3 into one of the original equation and solve for the other variable.

Step 5. Write the solution as an ordered pair.

Step 6. 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

Statistics

Decision Maths

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the system by elimination: $\{\begin{cases} 7 x + 8 y = 4 \\ 3 x - 5 y = 27 \end{cases}$