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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 9: Q89. (page 535)

Use elimination to solve each system of equations.
$2 x + y = 5 3 x 鈭� 2 y = 4$

Short Answer

Expert verified

The solution of the given system of equations is $(2, 1)$ .

Step by step solution

01

Step 1. Multiply.

Multiply each side $2 x + y = 5$ by 2.

$2 (2 x + y) = 2 (5) 4 x + 2 y = 10$

02

Step 2. Add.

Add $4 x + 2 y = 10$ and $3 x 鈭� 2 y = 4$ . Simplify to obtain the value of x.

$(4 x + 2 y) + (3 x 鈭� 2 y) = 10 + 4 7 x = 14 \frac{7 x}{7} = \frac{14}{7} x = 2$

03

Step 3. Substitute.

Substitute 2 for x into $2 x + y = 5$ and simplify.

$2 (2) + y = 5 4 + y 鈭� 4 = 5 鈭� 4 y = 1$

Therefore, the solution of the given system of equations is $(2, 1)$ .

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Most popular questions from this chapter

Graph each function. Find the y-intercept, and state the domain and range.

$y = 2^{x} 鈭� 3$

Which is an equation for the function shown in the graph?

A $y = 鈭� 2 x^{2}$

B $y = 2 x^{2} + 1$

C $y = x^{2} 鈭� 1$

D $y = 鈭� 2 x^{2} + 1$

Graph each function. Find the y-intercept, and state the domain and range.

$y = 2 {(5)}^{x}$

Write the equation for the nth term of each geometric sequence.

$3, 9, 27, . ....$

The cost of 5 notebooks and 3 pens is $\(9.75$ . The cost of 4 notebooks and 6 pens is $\) 10.50$ . Which of the following systems can be used to find the cost of a notebook $n$ and a pen $p$ ?

a. Write a system of equations to model the situation.

b. Solve the system of equations. How much does each item cost?

See all solutions

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