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Solve the following equations:$3x-2y=8; 4x+3y=5$.
Given :
The given equations are $3x-2y=8$ and $4x+3y=5$.
To do :
We have to solve the given equations.
Solution :
$3x-2y = 8$
Let it be equation (1).
$4x+3y = 5$
Let it be equation (2).
Multiply equation (1) by 4 and equation (2) by 3.
$4(3x-2y) = 4(8)$
$4(3x) -4(2y) = 32$
$12x-8y = 32$
Let it be equation (3).
$3(4x+3y) = 3(5)$
$3(4x)+3(3y) = 15$
$12x+9y=15$
Let it be equation (4).
Subtract equation (4) from equation (3),
$(12x-8y) - (12x+9y) = 32-15$
$12x-12x-8y-9y = 17$
$-17y=17$
$y=\frac{17}{-17}$
$y=-1$.
Substitute $y = -1$ in equation (1),
$3x-2(-1) = 8$
$3x+2=8$
$3x=8-2$
$3x=6$
$x=\frac{6}{3}$
$x=2$.
The value of x is 2 and y is $-1$.
Updated on: 10-Oct-2022
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