Answer:
a) x= 29, y= 87
b) x= 19, y= 45
Explanation:
Q5. a) Let the first number be x and the second number be y.
The sum of 2 integers is 116.
x +y= 116 -----(1)
The second number is three times the first number.
y= 3x -----(2)
Substitute (2) into (1):
x +3x= 116
4x= 116
x= 116 ÷4
x= 29
Substitute x= 29 into (2):
y= 3(29)
y= 87
b) Let the smaller number be x and the larger number be y.
x +y= 64 -----(1)
y -x= 26 -----(2)
Since we have to use substitution to solve the equations, let's first rewrite an equation to make one of the variables the subject of the equation.
From (1):
x= 64 -y -----(3)
Substitute (3) into (2):
y -(64 -y)= 26
y -64 +y= 26 (expand bracket)
2y= 26 +64 (simplify, +64 on both sides)
2y= 90
y= 90 ÷2
y= 45
Substitute y= 45 into (3):
x= 64 -45
x= 19