Chapter 4: Q 51. (page 386)

In the following exercises, solve the systems of equations by elimination.
$4 x - 3 y = 3 2 x + 5 y = - 31$

Short Answer

Expert verified

The solution for the system of linear equation is $(- 3, - 5)$ .

Step by step solution

Step 1. Given Information

System of linear equations:

$4 x - 3 y = 3 . . . . . . . . . (1) 2 x + 5 y = - 31 . . . . . . . . (2)$

Step 2. Calculation

Here both equations are in standard form. To get opposite coefficients of y multiply first equation with 5.

$5 (4 x - 3 y) = 5 (3) 20 x - 15 y = 15 . . . . . . . . (3)$

Also multiply second equation with 3.

$3 (2 x + 5 y) = 3 (- 31) 6 x + 15 y = - 93 . . . . . . . . . (4)$

Solve for x:

From equations $(3)$ and $(4)$ :

$20 x - 15 y = 15 6 x + 15 y = - 93 26 x = - 78 x = - \frac{78}{26} x = - 3$

Solve for y:

Substitute $x = - 3$

in the equation $4 x - 3 y = 3$ and solve for y.

$4 x - 3 y = 3 4 (- 3) - 3 y = 3 - 12 - 3 y = 3 - 3 y = 3 + 12 - 3 y = 15 y = \frac{15}{- 3} y = - 5$

The solution for the system of linear equation is $(- 3, - 5)$ .

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In the following exercises, solve the systems of equations by elimination.
$4 x - 3 y = 3 2 x + 5 y = - 31$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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In the following exercises, solve the systems of equations by elimination.4x-3y=32x+5y=-31

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, solve the systems of equations by elimination.
$4 x - 3 y = 3 2 x + 5 y = - 31$