Ch. 5 - Systems of Equations and Inequalities

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Blitzer 8th Edition

Ch. 5 - Systems of Equations and Inequalities

Problema 29

Capitolo 6, Problema 29

In Exercises 19–30, solve each system by the addition method. 3x = 4y + 1 3y = 1 - 4x

Guida verificata passo dopo passo

Rewrite both equations in standard form (Ax + By = C) to prepare for the addition method. For the first equation, subtract 4y and 1 from both sides to get

3x - 4 y = 1

. For the second equation, add 4x to both sides and subtract 1 from both sides to get

4 x + 3 y = 1

Align the two equations for addition:

3x - 4y = 1

and

4x + 3y = 1

Multiply each equation by a suitable number so that the coefficients of either

x

y

are opposites. For example, multiply the first equation by 3 and the second equation by 4 to align the coefficients of

y

3(3x - 4y) = 3(1)

and

4(4x + 3y) = 4(1)

Add the two resulting equations to eliminate

y

. This will give you an equation with only

x

. Solve this equation for

x

Substitute the value of

x

back into one of the original equations to solve for

y

. This completes the solution to the system.

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