Answer:
So the solution is x = -0.57 and y = 30/7.
Step By Step Explanation:
To solve a system of linear equations, such as "x = 8 - 2y" and "3x + y = 6", we can use substitution or elimination method.
Using substitution method:
solve one equation for one variable
substitute the expression obtained in step 1 into the second equation
solve the equation obtained in step 2 to find the value of the variable that was solved for
substitute this value back into the first equation to find the value of the other variable.
x = 8 - 2y;
3x + y = 6;
solve for x in the first equation
x = 8 - 2y
substitute the value of x in the second equation
3(8-2y) + y = 6
solve the second equation obtained for y
24 - 6y + y = 6
25 - 6y = 6
-6y = -19
y = 19/6
substitute the value of y back in the first equation
x = 8 - 2(19/6) = 8 - (38/6) = 8 - (63/6) = 8 - (63/6) = 8 - 10.5 = -2.5
So the solution is x = -2.5 and y = 19/6
Alternatively, using elimination method:
Add or subtract one equation from the other to eliminate one of the variables.
Solve the resulting equation for the remaining variable.
Substitute this value into either of the original equations to find the value of the eliminated variable.
Multiply the first equation by -3
-3x = -24 + 6y;
Add the above equation to the second equation
-3x + y = 6
-24 + 6y + y = 6
-24 + 7y = 6
7y = 30
y = 30/7
substitute the value of y into the first equation
x = 8 - 2(30/7) = 8 - (60/7) = 8 - (60/7) = 8 - 8.57 = -0.57
So the solution is x = -0.57 and y = 30/7.