Step-by-step explanation:
x+y=9
x=9-y ----------(i)
Now in second eqn put the value of x
2x -3y=8
2(9-y) - 3y=8
18 - 2y - 3y=8
18-8=5y
10=5y
y=2
Then put the value of y in eqn (i)
x=9-y
x=9-2
x=7
I hope this will be helpful for you.
Answer:
Step-by-step explanation:
Given,
x + y = 9
2x - 3y = 8
Using substitution method:
In this method , a variable is expressed in terms of another variable from one equation and it is substituted in the remaining equation.
[tex] \mathsf{x + y = 9}[/tex]
Move y to right hand side and change it's sign
⇒[tex] \mathsf{x = 9 - y}[/tex]⇔equation ( i )
Now, put the value of X from equation ( i )
⇒[tex] \mathsf{ 2 (9 - y) - 3y = 8}[/tex]
Distribute 2 through the parentheses
⇒[tex] \mathsf{18 - 2y - 3y = 8}[/tex]
Collect like terms
⇒[tex] \mathsf{18 - 5y = 8}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \mathsf{ - 5y = 8 - 18}[/tex]
Calculate
⇒[tex] \mathsf{ - 5y = - 10}[/tex]
Divide both sides of the equation by -5
⇒[tex] \mathsf{ \frac{ - 5y}{ - 5} = \frac{ - 10}{ - 5} }[/tex]
Calculate
⇒[tex] \mathsf{y = 2}[/tex]
Now, Put the value of y in the equation ( i )
⇒[tex]x = 9 - 2[/tex]
Calculate the difference
⇒[tex] \mathsf{x = 7}[/tex]
Hence, x = 7 and y = 2
The possible solution of the system is the ordered pair ( x , y )
[tex] \mathsf{(x \: , y \: ) = (7 , \: 2)}[/tex]
---------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
⇒[tex] \mathsf{7 + 2 = 9}[/tex]
⇒[tex] \sf{2 \times 7 - 3 \times 2 = 8}[/tex]
Simplify the equalities
⇒[tex] \sf{9 = 9}[/tex]
⇒[tex] \mathsf{8 = 8}[/tex]
Since all of the equalities are true , the ordered pair is the solution of the system.
[tex] \mathsf{ \underline{ \bold{(x \:, y \: ) = (7 \:, 2)}}}[/tex]
Hope I helped!
Best regards!!
