Which description best describes parallel lines?

Mathematics

2 answers:

Kipish [7]3 years ago

8 0

Straight lines going across

love history [14]3 years ago

3 0

Even lines,straight line

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Solve the following system of equations using the substitution method.

BartSMP [9]

Answer:

Step-by-step explanation:

First label the equations.

6x +3y= 18 -----(1)

y= -2x +5 -----(2)

subst. (2) into (1):

6x +3(-2x +5)= 18

6x +3(-2x) +3(5)= 18 (expand)

6x -6x +15= 18

15= 18 (simplify)

(reject)

There is no solution.

Further explanation:

If I rewrite the first equation into the form of y=mx+c, I would get

6x +3y=18

3y= 18 -6x (bring y term to one side)

y= 6- 2x (÷3 throughout)

y= -2x +6

Notice that the gradients of both lines are equal ( -2). This implies that they are parallel to each other and will never meet. Hence there are no solutions.

3 0

3 years ago

A metalworker has a metal alloy that is 15% copper and another alloy that is 75% copper. How many kilograms of each alloy shou

lisov135 [29]

48 kilograms of 15 % copper is combined with 72 kilograms of 75 % copper to create 120 kg of a 51% copper alloy

Solution:

Let "x" be the kilograms of 15 % copper

Then, (120 - x) be the kilograms of 75 % copper

Then, according to question,

"x" kilograms of 15 % copper is combined with (120 - x) kilograms of 75 % copper to create 120 kg of a 51% copper alloy

Thus we frame a equation as:

15 % of x + 75 % of (120 - x) = 51 % of 120

Solve the equation for "x"

$15 \% \times x + 75 \% \times (120-x) = 51 \% \times 120\\\\\frac{15}{100} \times x + \frac{75}{100} \times (120-x) = \frac{51}{100} \times 120\\\\0.15x + 0.75(120-x) = 0.51 \times 120\\\\0.15x + 90 - 0.75x = 61.2\\\\0.6x = 90 - 61.2\\\\0.6x = 28.8\\\\Divide\ both\ sides\ by\ 0.6\\\\x = 48$