Which ordered pair is a solution of the system?
1 answer:
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Answer:
The points for the given to linear equations is (5 , - 2) and (5 , - 1)
The points is plotted on the graph shown .
Step-by-step explanation:
Given as :
The two linear equation are
y = x - 1 ...........1
y = x - 6 ...........2
Now, Solving both the linear equations
Put the value of y from eq 2 into eq 1
I.e x - 6 =
x - 1
Or, x +
x = 6 - 1
Or, x = 5
or, x = 5
∴ x = 5
Now, Put the value of x in eq 1
So, y = x - 1
Or, y = × 5 - 1
or, y = - 1
Or, y = - 1 - 1
I.e y = -2
So, For x = 5 , y = - 2
Point is ( ,
) = (5 , - 2)
Again , put the value of x in eq 2
So, y = x - 6
Or, y = × 5 - 6
Or, y = - 6
Or, y = 4 - 6
I.e y = - 2
So, For x = 5 , y = - 2
Point is ( ,
) = (5 , - 2)
Hence, The points for the given to linear equations is (5 , - 2) and (5 , - 2)
The points is plotted on the graph shown . Answer
Answer:
x = 32 y = 16 z = 64
Step-by-step explanation:
x is the 1st number
y is the 2nd number
z is the 3rd number
The first number is twice the second number so
x = 2 y
The third number is twice the first number.
z = 2 x
Their sum is 112
x + y + z = 112
Plus in what we know:
x + y + z = 112
2 y + y + 2x = 112
3y + 2x = 112 Let's solve for y and subtract 2x from each side
3y = 112 - 2x Divide both sides by 3
y =
Now plug our answer back in to solve for x.
x = 2y
x = 2 ( )
x = (224 - 4x) / 3 Multiply each side by 3.
3x = 224 - 4x Add 4x to each side
3x + 4x = 224
7x = 224 Divide each side by 7
7x / 7 = 224 / 7
x = 32
Now we can solve for z.
z = 2x
z = 2 ( 32 )
z = 64
Now we can solve for the numerical value of y.
x + y + z = 112
32 + y + 64 = 112
96 + y = 112 Subtract 96 from each side.
y = 112 - 96
y = 16