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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 5: Q. 5.27 (page 600)

Solve the system by substitution.
$x + y = 6 y = 3 x - 2$

Short Answer

Expert verified

The solution set is $(2, 4)$ .

Step by step solution

01

Step 1. Given Information

We have to solve the system by substitution.

$x + y = 6 y = 3 x - 2$

02

Step 2. Putting the value of y from the second equation in the equation x+y=6.

$x + 3 x - 2 = 6 4 x - 2 = 6 Add 2 on both side 4 x - 2 + 2 = 6 + 2 4 x = 8 Divide by 4 on both side \frac{4}{4} x = \frac{8}{4} x = 2$

03

Step 3. Putting the value of x in the equation y=3x−2

$y = 3 \times 2 - 2 y = 6 - 2 y = 4$

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Most popular questions from this chapter

In the following exercises, translate to a system of equations and solve.

The difference of two supplementary angles is 88 degrees. Find the measures of the angles.

In the following exercises, solve the systems of equations by substitution.

$y = 3 x 6 x - 2 y = 0$

In the following exercises, solve the following systems of equations by graphing.

$\{\begin{cases} - 3 x + y = - 2 \\ 4 x - 2 y = 6 \end{cases}$

Alisha is making an $18$ ounce coffee beverage that is made from brewed coffee and milk. The number of ounces of brewed coffee is $5$ times greater than the number of ounces of milk. How many ounces of coffee and how many ounces of milk does Alisha need?

Determine whether an ordered pair is a solution of a system of equations. In the following exercises, determine if the following points are solutions to the given system of equations.

$\{\begin{cases} x + y = 1 \\ y = \frac{2}{5} x \end{cases}$

(a) $(\frac{5}{7}, \frac{2}{7})$

(b) $(5, 2)$

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