I need help with this problem

Solve system of equation algebraically y = 2x - 3 x + y = 18

natima [27]

Answer:

x = 7

y = 11

Step-by-step explanation:

Given the system;

y = 2x - 3

x + y = 18

1. Approach

The easiest way to solve this system of equations is to solve the second equation for the variable (y). Then add the systems, use algebra to solve for the value of (x), then substitute that value back into one of the original equations to solve for the value of (y). Another name for the method in use is the method of elimination, this is when a [erspm manipulates one of the equations in a system of the equation such that when they add the equations, one of the variables eliminatates. Thus, they can solve for the other variable and the backsolve for the value of the unknown variable.

2. Solve one of the equations for a variable

Manipulate the system such that each equation is solved for the same variable,

x + y = 18

Inverse operations,

x + y = 18

-18 -18

x + y - 18 = 0

-y -y

x - 18 = -y

3. Use elimination

Now substitute this back into the original system,

y = 2x - 3

-y = x - 18

Add the systems,

y = 2x - 3

-y = x - 18

_________

0 = 3x - 21

Inverse operations,

0 = 3x - 21

+21 +21

21 = 3x

/3 /3

7 = x

4. Find the value of the unknown variable

Backsovle to find the value of (y),

x + y = 18

Substitute,

7 + y = 18

Inverse operations,

7 + y = 18

-7 -7

y = 11

3 0

2 years ago

Read 2 more answers

Mike works two part time jobs while going to college. He works 8 and half hours a week at the ice-cream store for $10.55 per hou

Debora [2.8K]

Answer:

1.$186.63

2.$145.57

3.$7.27 more

4.65.65%

Step-by-step explanation:

Mike has two part time jobs.

Job 1: Ice-cream store

Number of hours worked= 8.5 hours

Payment per hour=$10.55

Job 2: Movie theater

Number of hours worked=7 hours

Payment per hour=$13.85

1. Earnings per week before taxes

⇒For job 1 will be; the product of hours worked and hourly payments

= 8.5×$10.55 =$89.68

⇒For job 2 will be;

=7×$13.85=$96.95

Total=$89.68+$96.95=$186.63

2. Calculate amount taken as tax

Find 22% of the amount earned

= 22/100 * 186.63 =$41.06

Remaining amount after tax will be;

=$186.63-$41.06=$145.57

3.

The job that Mike earns the most before taxes is at the Movie theater.

How much more will be; Earnings at Movie theater-Earnings at the Ice-cream store

=$96.95-$89.68

=$7.27 more

4.

After paying taxes the amount remaining is $145.57

After spending $50 on entertainment,the amount left will be;

$145.57-$50=$95.57

so to find the percent of remaining amount of Mike's paycheck will be;

95.57/145.57 *100=65.65%

5 0

3 years ago

Can u help me in this pls

Misha Larkins [42]

Answer:

The first one is correct I believe.

Step-by-step explanation:

6 0

3 years ago

Bought 8 gallons of gas for $22.32 how much would I pay for 11 gallons

Dmitrij [34]

Answer:

$30.69

Step-by-step explanation:

22.32/ 8 = 2.79

11 x 2.79 = 30.69

5 0

3 years ago

A right triangle with integer sides has area equal to 30. What is the length of its hypotenuse.

kozerog [31]

We have been given that a right triangle with integer sides has area equal to 30. We are asked to find the length of hypotenuse of right triangle.

We know that area of triangle is half the product of its base length and height.

Since our given triangle is a right triangle, so its base and height will be legs of right triangle.

$\frac{1}{2}\cdot\text{Base}\times \text{Height}=\text{Area}$

$\frac{1}{2}\cdot\text{Base}\times \text{Height}=30$

$\frac{1}{2}\cdot 2\cdot\text{Base}\times \text{Height}=30\cdot 2$

$\text{Base}\times \text{Height}=60$

This means that product of two bases is 60.

Now we need to find two multiples of 60 such that they are make a right triangle.

Multiples of 60:

1, 60

2, 30

3, 20

4, 15

5, 12

6, 10

We know that (5, 12 and 13) is a Pythagoras triplet.

$5^2+12^2=13^2$

$25+144=169$

$169=169$

Therefore, the hypotenuse of right triangle is 13 units.

8 0

3 years ago