Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system by substitution. {:[y=4x],[y=7x-30]:} (◻,◻)

Solve the system by substitution.\newliney=4xy=7x−30 \begin{array}{l} y=4 x \\ y=7 x-30 \end{array} \newline(□,□) (\square, \square)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Identify arithmetic and geometric sequencesright chevron icon

Full solution

Q. Solve the system by substitution.\newliney=4xy=7x−30 \begin{array}{l} y=4 x \\ y=7 x-30 \end{array} \newline(□,□) (\square, \square)
  1. Identify Equation to Substitute: First, we need to identify which equation to substitute into the other. Since the first equation is already solved for yy, we can substitute the expression for yy from the first equation into the second equation.\newlineSubstitute y=4xy = 4x into the second equation y=7x−30y = 7x - 30.
  2. Substitute Expression for y: Now we have 4x=7x−304x = 7x - 30. To find the value of xx, we need to solve this equation. Subtract 4x4x from both sides to get 0=3x−300 = 3x - 30.
  3. Solve for xx: Next, add 3030 to both sides to isolate the term with xx.3x=303x = 30.
  4. Isolate the Term with x: Now, divide both sides by 33 to solve for x.\newlinex=303x = \frac{30}{3}.\newlinex=10x = 10.
  5. Find Value of x: We have found the value of xx to be 1010. Now we need to substitute this value back into one of the original equations to find the value of yy. Let's substitute x=10x = 10 into the first equation y=4xy = 4x.
  6. Substitute xx into First Equation: Substitute xx with 1010 in the equation y=4xy = 4x.\newliney=4×10y = 4 \times 10.\newliney=40y = 40.
  7. Calculate Value of yy: We have found the value of yy to be 4040 when xx is 1010. This gives us the solution to the system of equations.\newlineThe solution is (x,y)=(10,40)(x, y) = (10, 40).

More problems from Identify arithmetic and geometric sequences

Question
Find the sum of the finite arithmetic series. ∑n=110(7n+4)\sum_{n=1}^{10} (7n+4)\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`
Get tutor helpright-arrow

Posted 2 months ago

Question
Type the missing number in this sequence: `2, 4 8`, ______,`32`
Get tutor helpright-arrow

Posted 2 months ago

Question
What kind of sequence is this? 2,10,50,250,…2, 10, 50, 250, \ldots Choices:Choices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the missing number in this pattern? 1,4,9,16,25,36,49,64,81,____1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Classify the series. ∑n=012(n+2)3 \sum_{n = 0}^{12} (n + 2)^3 \newlineChoices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the first three partial sums of the series.\newline1+6+11+16+21+26+⋯1 + 6 + 11 + 16 + 21 + 26 + \cdots\newlineWrite your answers as integers or fractions in simplest form.\newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the third partial sum of the series. \newline3+9+15+21+27+33+⋯3 + 9 + 15 + 21 + 27 + 33 + \cdots\newlineWrite your answer as an integer or a fraction in simplest form. \newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the first three partial sums of the series. \newline1+7+13+19+25+31+⋯1 + 7 + 13 + 19 + 25 + 31 + \cdots\newlineWrite your answers as integers or fractions in simplest form. \newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 3 months ago

Question
Does the infinite geometric series converge or diverge?\newline1+34+916+2764+⋯1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots\newlineChoices:\newline[A]converge\text{[A]converge}\newline[B]diverge\text{[B]diverge}
Get tutor helpright-arrow

Posted 2 months ago

View all (33)