complete table for the following equation
2x+y=9
x y
-3
1
4
5
-1
2 x + y = 9 Subtract 2x to both sides
2 x + y - 2 x = 9 - 2 x
y = 9 - 2 x
y = - 2 x + 9
Now put x values in this formula
x = - 3
y = - 2 x + 9 = - 2 * ( - 3 ) + 9 = 6 + 9 = 15
x = - 3 , y = 15
x = 1
y = - 2 x + 9 = - 2 * 1 + 9 = - 2 + 9 = 7
x = 1 , y = 7
x = 4
y = - 2 x + 9 = - 2 * 4 + 9 = - 8 + 9 = 1
x = 4 , y = 1
x = 5
y = - 2 x + 9 = - 2 * 4 + 9 = - 10 + 9 = - 1
x = 5 , y = - 1
x = - 1
y = - 2 x + 9 = - 2 * ( - 1 ) + 9 = 2 + 9 = 11
x = - 1 , y = 11
x = 5
y = - 2 x + 9 = - 2 * 5 + 9 = - 10 + 9 = - 1
x = 5 , y = - 1
To complete the table for the equation 2x + y = 9, we need to find the corresponding values of x and y that satisfy the equation.
We can solve the equation for y by isolating it on one side:
2x + y = 9
Subtract 2x from both sides:
y = 9 - 2x
Now we can substitute different values of x into the equation to find the corresponding value of y.
For the first row, let's start with x = -3:
y = 9 - 2(-3)
y = 9 + 6
y = 15
So, for x = -3, the corresponding value of y is 15.
For the second row, let's use x = 1:
y = 9 - 2(1)
y = 9 - 2
y = 7
Therefore, for x = 1, y = 7.
For the third row, let's use x = 4:
y = 9 - 2(4)
y = 9 - 8
y = 1
Hence, for x = 4, y = 1.
For the fourth row, let's calculate when y = 5:
5 = 9 - 2x
Now, isolate x on one side of the equation:
2x = 9 - 5
2x = 4
x = 4/2
x = 2
So when y = 5, x = 2.
For the fifth row, let's calculate when y = -1:
-1 = 9 - 2x
Isolate x on one side:
2x = 9 + 1
2x = 10
x = 10/2
x = 5
Thus, when y = -1, x = 5.
Now let's complete the table:
x y
-3 15
1 7
4 1
2 5
5 -1