"find each value of a and b solving..." solved and explained

High School
Algebra
Algebra I
Exponents and radicals

Joni Kenny

Answered question

2021-03-06

find each value of a and b solving the linear equations
$x - w = 2$
$y - z + w = 3$
$a z = 1$
$y + b w = 0$

Answer & Explanation

Isma Jimenez

Skilled2021-03-07Added 84 answers

Given linear equations are,
$x - w = 2, y - z + w = 3, a z = 1, y + b w = 0$
Step 2
To find values of a and b.
Given equations are
$x - w = 2. . . (1)$
$y - z + w = 3. . . (2)$
$a z = 1. . . (3)$
$y + b w = 0. . . (4)$
from equation(3) $z = \frac{1}{a}$
from equation(1) $w = x - 2$
substitute value of z and $w i n (2)$
$y - 1 a + x - 2 = 3$
$\Rightarrow a y - 1 + a x - 2 a + 3 a$
$\Rightarrow a y - 1 + a x - 5 a = 0$
$\Rightarrow a y + a x - 5 a = 1$
$\Rightarrow a (y + x - 5) = 1$
$\Rightarrow a = \frac{1}{(y + x - 5)}$
from equation (4) $y + b w = 0 \Rightarrow y = - b w$
$\Rightarrow b = \frac{- y}{w}$
substitute $w = x - 2 i n b = \frac{- y}{w}$
$\Rightarrow b = \frac{- y}{x - 2}$
Therefore the values of a and b are
$a = \frac{1}{y + x - 5}, b = \frac{- y}{x - 2}$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Algebra I

Didn't find what you were looking for?