Ch. 5 - Systems of Equations and Inequalities

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Blitzer 8th Edition

Ch. 5 - Systems of Equations and Inequalities

Problema 21

Capitolo 6, Problema 21

In Exercises 19–30, solve each system by the addition method. 2x + 3y = 6 2x - 3y = 6

Guida verificata passo dopo passo

Write down the system of equations clearly:

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

Add the two equations together to eliminate

y

because the coefficients of

y

are opposites (+3y and -3y). This gives:

(2x + 3y) + (2x - 3y) = 6 + 6

Simplify the left side by combining like terms:

2x + 2x + 3y - 3y = 4x + 0 = 4x

, and simplify the right side:

6 + 6 = 12

. So the equation becomes

4x = 12

Solve for

x

by dividing both sides by 4:

x = \(\frac{12}{4}\)

Substitute the value of

x

back into one of the original equations to solve for

y

. For example, use

2x + 3y = 6

, plug in

x

, and solve for

y

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