All categories

1 year ago

Solve the system of equations. 5x y = 9 3x 2y = 4 (−2, 5) (1, 4) (2, −1) (4, −4)

Mathematics

1 answer:

kobusy [5.1K]1 year ago

6 0

The solution of the system of equations that is given is (2,-1).

Given a system of equations are 5x+y=9 and 3x+2y=4.

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied.

The given equations are

5x+y=9 ......(1)

3x+2y=4 ......(2)

Here, the substitution method is used to solve the system of equations.

Find the value of y from equation (1) by subtracting 5x from both sides.

5x+y-5x=9-5x

y=9-5x

To find the value of x substitute the value of y in equation (2).

3x+2(9-5x)=4

Apply the distributive property a(b+c)=ab+ac as

3x+2×9-2×5x=4

3x+18-10x=4

Combine the like terms on the left side as

-7x+18=4

Subtract 18 from both sides and get

-7x+18-18=4-18

-7x=-14

Divide both sides by -7 and get

(-7x)÷(-7)=(-14)÷(-7)

x=2

Substitute the value of x in equation (1) and get

5(2)+y=9

10+y=9

Subtract 10 from both sides

10+y-10=9-10

y=-1

Hence, the solution of system of equations 5x+y=9 and 3x+2y=4 is (2,-1).

Learn more about system of equations from here brainly.com/question/13729904

#SPJ4

You might be interested in

Determine the arithmetic sequence if the fourth term is negative six and the eleventh term is negative thirty four

ICE Princess25 [194]

An arithmetic sequence takes the form

$a_n=a_{n-1}+d$

where $d$ is the common difference between terms. You can solve for $a_n$ in terms of any of the previous terms of the sequence:

$a_n=a_{n-1}+d\implies~a_n=a_{n-2}+2d\implies~a_n=a_{n-3}+3d\implies\cdots\implies~a_n=a_{n-k}+kd$

for some integer $1\le k\le n-1$

Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term $a_1$

$a_n=a_1+(n-1)d$

Given that the 4th term is $a_4=-6$ and the 11th term is $a_{11}=-34$ , you have the following system of equations.

$\begin{cases}-6=a_1+(4-1)d\\-34=a_1+(11-1)d\end{cases}$

Solving this system for the two unknowns yields $a_1=6$ and $d=-4$ .

So, the sequence is given explicitly by

$a_n=6+(n-1)(-4)=-4n+5$

3 0

2 years ago

What times itself 3 times to get -0.125

Verdich [7]

That would be -0.041

-0.125/3 = -0.041666666

5 0

2 years ago

one number is 1 more than 2 times another. if their sum is increased by sevan, the result is twenty six

Lady bird [3.3K]

the numbers are 6 and 13

let x be one of the numbers then the other is 2x + 1

their sum increased by 7 = 26

x + 2x + 1 + 7 = 26

3x + 8 = 26

subtract 8 from both sides

3x = 26 - 8 = 18

divide both sides by 3

x = $\frac{18}{3}$ = 6

the numbers are 6 and (2 × 6) + 1 = 12 + 1 = 13

7 0

2 years ago

Complete the following proofs.

Studentka2010 [4]

Answer:

Points R, S, T, Q on circle O is given

and points are central arc

Step-by-step explanation:

5 0

2 years ago

Can some one help me with this question its hard :( down below ill give brainliest

Pani-rosa [81]

The answer is B x^2 y

3 0

2 years ago