Respuesta :
Answer:
X = ( 40/11 )
Y = ( -58/11 )
Step-by-step explanation:
6x + 3y = 6
7x + 9y = -22
-------------------------
-3(6x + 3y = 6)
= -18x - 9y = -18
-------------------------
-18x - 9y = -18
7x + 9y = -22
-11x = -40
÷-11 ÷-11
x = ( 40/11 )
------------------------
6( 40/11 ) + 3y = 6
( 240/11 ) + 3y = 6
-( 240/11 ) -( 240/11 )
3y = ( -174/11 )
÷3 ÷3
y = ( -58/11 )
---------------------------
I hope this helps!
Answer:
[tex]x=\frac{40}{11}[/tex]
[tex]y=-\frac{58}{11}[/tex]
Step-by-step explanation: [tex]\left \{ {{6x+3y=6} \atop {7x+9y=-22}} \right.[/tex]
Multiply both sides of the equation by a coefficient
[tex]\left \{ {{3\left(6x+3y\right)=6\times3} \atop {7x+9y=-22}} \right.[/tex]
Apply the Distributive Property
[tex]\left \{ {{18x+9y=6\times3} \atop {7x+9y=-22}} \right.[/tex]
Calculate the product or quotient
[tex]\left \{ {{18x+9y=18} \atop {7x+9y=-22}} \right.[/tex]
Subtract the two equations
[tex]18x+9y-(7x+9y)=18-(-22)[/tex]
Remove parentheses
[tex]18x+9y-7x-9y=18+22[/tex]
Cancel one variable
[tex]18x-7x=18+22[/tex]
Combine like terms
[tex]11x=18+22[/tex]
Calculate the sum or difference
[tex]11x=40[/tex]
Divide both sides of the equation by the coefficient of variable
[tex]x=\frac{40}{11}[/tex]
Substitute into one of the equations
[tex]7\times\frac{40}{11}+9y=-22[/tex]
Write as a single fraction
[tex]\frac{7\times40}{11}+9y=-22[/tex]
Calculate the product or quotient
[tex]\frac{280}{11}+9y=-22[/tex]
Multiply both sides of the equation by the common denominator
[tex]\frac{280\times11}{11}+9y\times11=-22\times11[/tex]
Reduce the fractions
[tex]280+9y\times11=-22\times11[/tex]
Multiply the monomials
[tex]280+99y=-22\times11[/tex]
Calculate the product or quotient
[tex]280+99y=-242[/tex]
Rearrange variables to the left side of the equation
[tex]99y=-242-280[/tex]
Calculate the sum or difference
[tex]99y=-522[/tex]
Divide both sides of the equation by the coefficient of variable
[tex]y=-\frac{522}{99}[/tex]
Cross out the common factor
[tex]y=-\frac{58}{11}[/tex]
The solution of the system is
[tex]\left \{ {{x=\frac{40}{11}} \atop {y=-\frac{58}{11}}} \right.[/tex]
I hope this helps you
:)
