Solve the system of equations x+2y=-16 and x+6y=-28 by combining the equations.

Mathematics

2 answers:

baherus [9]3 years ago

8 0

Answer:

x = -10

y = -3

Step-by-step explanation:

When combining the equations, we must ensure that one of the two variables will cancel out. The easiest way to do this will be to multiply one of the equations by -1, such that the x will cancel out once they are added together. This can be done with either equation, but I will do it for the first one.

This gives us the system:

$\left \{ {{-x-2y=16} \atop {x+6y=-28}} \right.$

We can then add the two equations by combining each of the terms:

$(x - x) + (6y - 2y) = (-28 + 16)\\(0) + (4y) = (-12)\\4y = -12\\y = -3$

Now that we have the value for y, we substitute it back into any of the original equations and solve for x:

$x + 2y = -16\\x + 2(-3) = -16\\x - 6 = -16\\x = -10$

To check our work, we substitute both x and y into the other original equation:

$x + 6y = -28\\(-10) + 6(-3) = -28\\-10 - 18 = -28\\-28 = -28$

Gnesinka [82]3 years ago

3 0

Answer:

x= -18 y=-5/3

Step-by-step explanation:

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A restaurant charges an automatic gratuity of 18% on tables with more than 6 people. A party of 8 had a bill of p. Which express

Nuetrik [128]

The expression of total cost of bill for party by 8 people in the restaurant including the gratuity amount is 1.18p.

<h3>How to write algebraic expression? </h3>

Algebraic expression are the expression which consist the variables, coefficients of variables and constants.

The algebraic expression are used represent the general problem in the mathematical way to solve them.

Steps to write down the simple algebraic expression-

Identify all the factors of the expression.

Assume a variable for the changing values.

Put a coefficient for the variable, if there is any rate of change of variable.

Use constant numbers for the fixed values.

Given information-

The automatic gratuity charges by restaurant is of 18 percent for more than 6 people on a table.

The number of people party in the restaurant is 8.

The bill amount of the 8 people for party in the restaurant is p.

Here, automatic gratuity charged by restaurant is of 18 percent for more than 6 people on a table

As the number of people party in the restaurant is 8 therefore the automatic gratuity charged by restaurant on the bill amount of p is should be 18 percent of it.

The 18 percent of bill p is,

$p\times\dfrac{18}{100} =0.18p$

Thus the gratuity charged by restaurant on the bill amount of p is 0.18 p.

Suppose the expression which is used to find the total cost of the meal with the gratuity is $f(p)$ .

Now the total bill amount should be equal to the sum of bill amount and gratuity amount. Thus, total cost of the meal with the gratuity is,

$f(p)=p+0.18p\\f(p)=1.18p$