4 times one number plus 3 times the other is 78. 3 times the first number minus 8 times the other is -45. What are the numbers?

the first number is 11 38/41

The second number is 10 4/41

Step-by-step explanation:

Let x represent the first number.

Let y represent the second number.

4 times one number plus 3 times the other is 78. It means that

4x + 3y = 78- - - - - - - - - -1

3 times the first number minus 8 times the other is -45. It means that

3x - 8y = - 45- - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 3 and equation 2 by 4. It becomes

12x + 9y = 234

12x - 32y = - 180

Subtracting, it becomes

41y = 414

y = 414/41

y = 10 4/41

Substituting y = 414/41 into equation 1, it becomes

4x + 3 × 414/41 = 78

4x + 1242/41 = 78

4x = 78 - 1242/41

4x = 1956/41

x = 1956/41 × 1/4

x = 1956/164

x = 11 38/41

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.