Answer:
Rewrite the first equation as x = 36 – 3y.
Step-by-step explanation:
x + 3y = 36 (1)
4x + 5y = 9 (2)
Using substitution method
From (1)
x = 36 - 3y
Substitute x = 36 - 3y into (2)
4x + 5y = 9
4(36 - 3y) + 5y = 9
144 - 12y + 5y = 9
- 12y + 5y = 9 - 144
-7y = -135
y = -135 / -7
y = 19.3
There is an error with the second equation, 4x + 5y can not be equal to 9
Nevertheless, the first step when solving by substitution is:
Rewrite the first equation as
x = 36 – 3y.
Answer:
Step-by-step explanation:
Consecutive integers just means like one after another.
This means that:
First number = x
Second number = x + 1
Third number = x + 2
They've told us that the sum of 3 consecutive integers is 78.
First number + second number + third number = 78
Sub the equations we wrote into the formula above and we get:
x + x + 1 + x + 2 = 78
Gather the like terms.
3x + 3 = 78
Subtract 3 from both sides.
3x = 78-3 = 75
Divide both sides by 3 to solve for x.
x = 75/3 = 25
If you look at the very beginning we said that the first number = x.
Therefore it is 25.
Second number = x + 1 = 26
Third number = x + 2 = 27
There are several shapes that fulfill these requirements. All involve to parallel rows of 4, then the other two trees forming a perpendicular for (using a tree from each of the other two rows).
E.g.
X X X X
X X X X
X
X
X X X X
X
X
X X X X
X X X X
X
X X X X
X
We know that m ║ n.
Let's first find the value 'x'.
When two lines are parallel, and a transversal is drawn, the angles on the same side of the transversal are equivalent.
This means that (5x + 16)° and (7x + 4)° are equivalent.
Equating them,
5x + 16 = 7x + 4
16 - 4 = 7x - 5x
12 = 2x
x = 12/2
x = 6°
Since we know the value of 'x', let's substitute them into the angles and find out the actual measurements.
5x + 16 = 5 × 6 + 16 = 30 + 16 = 46°.
7x + 4 = 7 × 6 + 4 = 42 + 4 = 46°.
Now let's find the value of 'y'.
If you observe carefully, (7x + 4)° and (y + 6)° form a linear pair.
This means that both those angles should add upto 180°.
Using that theory, the following equation can be framed:
(y + 6)°+ (7x + 4)° = 180°
Since we know the actual value of (7x + 4)°, let's substitute that value and move ahead.
(y + 6)° + 46° = 180°
y + 6 + 46° = 180
y + 52° = 180°
y = 180° - 52°
y = 128°
Therefore, the values of 'x' and 'y' are 46° and 128° respectively.
Hope it helps. :)