Answer:
1. The two numbers are 56 and 15
2. The two angles are 56 and 34 degrees
3. The two angles are 110 and 70 degrees
4.The largest number is -10
Step-by-step explanation:
Solving (1):
Represent both numbers with x and y
[tex]x = 11 + 3y[/tex]
[tex]x + y = 71[/tex]
Solving for x and y
Substitute [tex]11 + 3y[/tex] for x in the second equation
[tex]11 + 3y + y = 71[/tex]
Collect Like Terms
[tex]3y + y =71 - 11[/tex]
[tex]4y = 60[/tex]
Divide both sides by 4
[tex]y = 15[/tex]
Recall that
[tex]x = 11 + 3y[/tex]
[tex]x = 11 + 3 * 15[/tex]
[tex]x = 56[/tex]
Hence, the two numbers are 56 and 15
Solving (2)
Represent the two angles with x and y
[tex]x = 22 + y[/tex]
Since they are complementary;
[tex]x + y = 90[/tex]
Substitute 22 + y for x in [tex]x + y = 90[/tex]
[tex]22 + y +y= 90[/tex]
[tex]22 + 2y =9 0[/tex]
Collect Like Terms
[tex]2y = 90 - 22[/tex]
[tex]2y = 68[/tex]
Divide both sides by 2
[tex]y = 34[/tex]
Recall that [tex]x = 22 + y[/tex]
[tex]x = 22 + 34[/tex]
[tex]x = 56[/tex]
Solving (3):
Represent the two angles with x and y
[tex]x = 40 + y[/tex]
Since they are supplementary;
[tex]x + y = 180[/tex]
Substitute 40 + y for x in [tex]x + y = 180[/tex]
[tex]40 + y + y = 180[/tex]
[tex]40 + 2y = 180[/tex]
Collect Like Terms
[tex]2y = 180 - 40[/tex]
[tex]2y = 140[/tex]
Divide both sides by 2
[tex]y = 70[/tex]
Recall that [tex]x = 40 + y[/tex]
[tex]x = 40 + 70[/tex]
[tex]x = 110[/tex]
Solving (4):
Let the smallest number be x
[tex]x + x + 2 + x + 4 = -36[/tex]
Collect Like Terms
[tex]x + x + x = -36 - 2 - 4[/tex]
[tex]3x =-42[/tex]
Divide through by 3
[tex]x = -14[/tex]
The largest number; x + 4 is
[tex]x + 4 = -14 + 4[/tex]
[tex]x + 4 = -10[/tex]
Hence, the largest number is -10
