The solution to the system of equations is x = 8, y = 4.
<h3>
How to write the system of equations?</h3>
First, let's define our variables as x and y.
"the sum of two numbers is twelve" is written as:
x + y = 12
"two times the first number minus three times the second number is four" is written as:
2x - 3y = 4
Then the system of equations is:
x + y = 12
2x - 3y = 4
<h3>How to solve it?</h3>
First, we isolate one of the variables in one equation, I will isolate x on the first one to get:
x = 12 - y
Now we replace this on the other equation, so we get:
2*(12 - y) - 3y = 4
Now we can solve this for y.
24 - 2y - 3y = 4
24 - 5y = 4
24 - 4 = 5y
20/5 = y = 4
Now we know the value of y, and:
x = 12 - y = 12 - 4 = 8
Then the solution of the system is:
x = 8, y = 4.
If you want to learn more about systems of equations, you can read:
brainly.com/question/13729904
Y^8/y^5
When multiplying exponents with the same base, you add the exponents
Answer:
2. x = 2 & y = 4
3. x = 4 & y = 2
Step-by-step explanation:
2. x + y = 6
2x + y = 8 (multiply the first equation by -1, so you can eliminate the ys)
- x - y = -6
2x + y = 8 (now add the variables together)
x = 2 (plug in x in one of the equations to find out y)
x + y = 6
(2) + y = 6
-2 -2
y = 4
3. 3x + y = 14
x = 2y (plug in x into the first equation and solve it for y)
3(2y) + y = 14
6y + y = 14
7y = 14
y = 2 (plug in y in one of the equations to find out x)
x = 2y
x = 2(2)
x = 4
4. One number (x) is 2 more (+2) than twice (times 2) as large as another. their sum is 17. Find the numbers.
2x + 2 = 17 (solve for x)
-2 -2
2x = 15
x = 7.5
6. 7 (4x + 1) - (x + 6) (start by distributing 7 into the first parenthesis)
(28x + 7) - (x + 6) (do the same to the other parenthesis by distributing -1)
(28x + 7) (-x - 6) (and now just combine like terms)
28x + 7 - x - 6
28x - x + 7 - 6
27x + 1
i hope this helped! if you have any question, pls let me know!
Answer:
X=6
Y= -1
Step-by-step explanation:
We have measures of all tree sides of the both triangles,
so we can use SSS to check if the triangles are similar.
|ED|/|AB| =5/10=1/2
|DC|/|BC| = 4/8 = 1/2
|EC|/|AC| = 6/12 = 1/2
We see that all tree pairs are in proportion, so these triangles ΔABC and ΔEDC are similar.
We have enough information to prove that ΔABC similar to ΔEDC.
