Answer:
I. x = -3
II. y = -2
Explanation:
Given the following algebraic equation;
[tex] -6x + 5y = 8 [/tex] .........equation 1
[tex] 2x - 4y = 2 [/tex] ..........equation 2
We would solve the algebraic equation using the substitution method
From equation 1;
[tex] 5y = 8 + 6x [/tex]
[tex] y = \frac {8 + 6x}{5} [/tex] .....equation 3
Substituting eqn 3 into eqn 2, we have;
[tex] 2x - 4(\frac {8 + 6x}{5}) = 2 [/tex]
[tex] 2x - \frac{32 + 24x}{5} = 2 [/tex]
Multiplying all through by 5
[tex] 10x - 32 - 24x = 10 [/tex]
Rearranging the equation, we have:
[tex] 10x - 24x = 10 + 32 [/tex]
[tex] -14x = 42[/tex]
[tex] x = \frac {-42}{14} [/tex]
x = -3
Next we find the value of y;
From eqn 3;
[tex] y = \frac {8 + 6x}{5} [/tex]
Substituting the value of "x" into the equation, we have;
[tex] y = \frac {8 + 6*(-3)}{5} [/tex]
[tex] y = \frac {8 - 18}{5} [/tex]
[tex] y = \frac {-10}{5} [/tex]
y = -2
