The solution to given system of equations are 
<em><u>Solution:</u></em>
Given that we have to find solution to the system of equations
<em><u>Given equations are:</u></em>
x + 2y = 10 ------ eqn 1
y = 12x + 3 ------ eqn 2
We can solve the above equations by substitution method
<em><u>Substitute eqn 2 in eqn 1</u></em>
x + 2(12x + 3) = 10
x + 24x + 6 = 10
25x = 10 - 6
25x = 4
<em><u>Substitute the above value of x in eqn 2</u></em>
Thus the solution to given system of equations are
#42.
14n - 32 = 22
add 32 to both sides
14n - 32 + 32 = 22 + 32
simplify
14n = 54
divide both sides by 14
14n/14 = 54/14
simplify
n = 3 12/14
n = 3 6/7 or n = 3.857
8 is missing for the table
The shapes are similar.
When two figures are similar, the ratios of the lengths of their corresponding sides are equal.
Therefore,
Simplify:
Cross multiply:
42(10+x) = 57x
420 + 42x = 57x
420 = 57x - 42x
420 = 15x
x = (420÷15)
x = 28
5)
Equilateral triangle, all sides are equal
So 2x + 5 = 11
2x = 6
x = 3
Answer is the first one
3; Equilateral theorem
6)
Isosceles triangle has at least two congruent sides.
So 6x = 24
x = 4
Answer x = 4
Converse of the Base Angle Theorem
7)
5x + 7 = 52
5x = 45
x = 9
Answer
x = 9
Base angle theorem
8)
5y - 14 = 3y
2y = 14
y = 7
Answer
7; Equiangular theorem
