Respuesta :
Explanation:
Consider the following system of linear equations:
Equation 1:
[tex]5x-4y=-30[/tex]Equation 2:
[tex]-2x+y=9[/tex]From equation 2, we can solve for y and obtain the following equation:
Equation 3:
[tex]y=9+2x[/tex]Now, replacing this in equation 1, we get:
[tex]5x-4(9+2x)=-30[/tex]applying the distributive property, we get:
[tex]5x\text{ - 36 - 8x = -30}[/tex]putting like terms together, we obtain:
[tex]5x\text{ - 8x = -30 + 36}[/tex]this is equivalent to:
[tex]\text{ - 3x = 6}[/tex]solving for x, we get:
[tex]x=\text{ -}\frac{6}{3}=\text{ - 2}[/tex]Now, replacing this value in equation 3, we get:
[tex]y=9+2x=\text{ 9 + 2\lparen-2\rparen= 9 - 4 = 5}[/tex]we can conclude that the correct answer is:
Answer:The solution of the given system of linear equations is:
( x , y ) = ( - 2, 5 )
then
x= - 2
and
y = 5
