Solving Linear Systems with Substitution - Definition & Examples
Read this topicExplanations 4
- Earlier, we saw how to solve a system of linear equations by graphing. Later, you will look at solving systems via elimination. After you master graphing, substitution, and elim…
By Catherine Yeo, Andrew Wang, Andrew Zoerb, Alex Federspiel, Jonathan Heller, Caroline K, Anusha Rahman
- (Video) The Decision - Math Video Challenge by PBSQ with the MATHCOUNTS Foundation Let's warm up with the winning video from the 2015 MATHCOUNTS Math Video Challenge! This video…
By Expii Solve, Zora Gilbert, Alex Federspiel, Amy Feraco, Caroline K, Jonathan Heller, Anusha Rahman
- (Video) Solving Systems of Equations with the Substitution Method by NancyPi This video by NancyPi explains systems of equations and substitution. Summary\large{\text{Summary}}S…
By Stefan Cuevas, Zora Gilbert, Alex Federspiel, Amy Feraco, Caroline K, Jonathan Heller, Anusha Rahman
- A system of equations is "two or more equations that have the same variables with the same values." The relationship between equations in a system is pretty cool. You can substi…
By Hannah Bonville, Zora Gilbert, Alex Federspiel, Amy Feraco, Caroline K, Jonathan Heller
Problems 45
- What is the ratio of the number of bicycles to the number of tricycles in the garage?
- Cassidy has 161616 pets which consist of cats and dogs. Each dog weighs on average 606060 lbs and eats one small bag of dog food, which costs \2.25 a bag. Each cat weighs on ave…
- Zack is shooting a short film and needs a lot extras for a scene. The scene takes place inside a building that has a maximum occupancy of 400400400. For every crew member there …
- Solve the system of equations using substitution. 4x+3y=18x+2y=6\begin{gather}4x+3y=18\\ x+2y=6\end{gather}4x+3y=18x+2y=6
- Solve the system of equations using substitution. 2x+2y=82x+2y=82x+2y=8 6x+12y=306x+12y=306x+12y=30
- Solve the system of equations using substitution. x−4y+2z=10x-4y+2z=10x−4y+2z=10 6x+6y−6z=186x+6y-6z=186x+6y−6z=18 z−x−12y=30z-x-12y=30z−x−12y=30
- Solve the system of equations using substitution. x−y=4x-y=4x−y=4 2x+y=82x+y=82x+y=8 If the solution is (x,y)(x,y)(x,y), enter in the value of 10x+y10x + y10x+y as your answer.
- Solve the system of equations using substitution. 3x−y=63x-y=63x−y=6 2y−4x=122y-4x=122y−4x=12 If the solution is (x,y)(x,y)(x,y), enter in the value of 100x+y100x + y100x+y as y…
- Solve using substitution. 5x+6y=−305x+6y=-305x+6y=−30 3x2−5y=11\frac{3x}{2}-5y=1123x−5y=11
- Find xxx given the two equations: 3x+2y=104x+y=6\begin{gather}3x+2y=10\\ 4x+y=6\end{gather}3x+2y=104x+y=6
- A 645645645 mile, 666 hour plane trip was flown at two speeds. For the first part, the average speed was 959595 mph. Then the tailwind picked up and the second part was made in …
- Anna and Cooper each leave the same house at 2:382{:}382:38 p.m. on a Saturday in the middle of July. The average speed of Anna's car is 323232 mph slower than twice the speed o…
- There is a point (a,b)(a,b)(a,b) on the line 2x+3y=122x+3y=122x+3y=12 where the xxx-coordinate is 32\frac3223 of the yyy-coordinate. Enter in the value of 10a+b10a + b10a+b as …
- A bunch of bicycles and tricycles move past you, and you count the number of wheels that go by. Eventually, you count 101010 vehicles with a total of 232323 wheels. How many of …
- For which values of aaa does the following system of equations have no solution (x,y)(x,y)(x,y)? {y=ax+2y=(2a−3)x+4\begin{cases} y = ax + 2 \\ y = (2a-3)x + 4 \end{cases}{y=ax+2…
- Andrea and Lauren are 202020 kilometers apart. They bike toward one another with Andrea traveling three times as fast as Lauren, and the distance between them decreasing at a ra…
- Let fff be a quadratic function with roots aaa and bbb. Assume fff is shifted right by 101010 units, and now has roots 3a+43a + 43a+4 and 2b−12b - 12b−1 (NOT necessarily in that…
- The Fibonacci numbers are defined recursively by the equation Fn=Fn−1+Fn−2F_n = F_{n - 1} + F_{n - 2}Fn=Fn−1+Fn−2 for every integer n≥2n \ge 2n≥2, with initial values F0=0F_0…
- The triangle ABCABCABC lies on the coordinate plane. The midpoint of AB‾\overline{AB}AB has coordinates (−16,−63)(-16, -63)(−16,−63), the midpoint of AC‾\overline{AC}AC has coor…
- Nate has a busy day ahead of him. He has marine training, video games with friends, work, and sleep (not necessarily in that order). He also needs to sleep twice as much as the …
- Cooper is finally writing a novel. The number of chapters, the number of sub-chapters, and the number of pages sum to be 840840840. He also knows that there are 444 times as man…
- Josh's new laptop screen has a width 22 inches less than twice the length. The perimeter is at least 46 inches. Find the minimum dimensions of the laptop's screen in integers.
- A PS4 and a game cost at least 400\400400. The PS4 costs 160\160160 more than four times the price of the game. What is the least amount the game could cost?
- Tony is deciding between two phone plans. In Plan A, he is charged a one-time initial fee of 55.00 dollars and must pay 70 dollars per month. In Plan B, he is charged 85 dollars…
- Mary and David are 833833833 miles apart and are heading toward each other to meet for dinner. Mary is traveling at 545454 mph and David is traveling at 656565 mph. How long wil…
- Which step is missing in solving the following system of equations by substitution? 3x−2y=76x+y=6\begin{gather}3x - 2y = 7\\ 6x + y = 6\end{gather}3x−2y=76x+y=6 Solution: x=7+…
- Using 17x−4y=3417x - 4y = 3417x−4y=34, what is xxx in terms of yyy?
- Which of the following is not a step in solving the following system of linear equations by substitution? ax+by=cax + by = cax+by=c ax+ey=fax + ey = fax+ey=f Assume that a,b,e≠0…
- If we use 4x−2y=84x - 2y = 84x−2y=8, what is yyy in terms of xxx?
- Suki is going to play field hockey. She can either bring a stick and 111 ball, or no stick and 333 balls. Assume that on her team of 555, every player can bring one of the same …
- After successfully figuring out how to clone dinosaurs, you and your colleagues decide to build a theme park in order to show them off to the public (sounds like a perfectly saf…
- Write a system of equations using the information above and use the substitution method to solve it.
- How many pizzas should be ordered?
- Admission to the local carnival is 7.50\7.507.50 for adults and 5.50\5.505.50 for children. On the fourth of July 2,5002{,}5002,500 people attended the carnival and the carnival…
- Solve the system of equations using substitution. x=1+yy=1−x\begin{gather} x=1+y\\ y=1-x \end{gather}x=1+yy=1−x If the solution is (x,y)(x,y)(x,y), enter in the value of 10x+y…
- Solve the system of equations using substitution. 3x+y=10x+8y=11\begin{gather} 3x+y=10\\ x+8y=11 \end{gather}3x+y=10x+8y=11 If the solution is (x,y)(x,y)(x,y), enter in the va…
- Solve the system of equations using substitution. 2x+y=24x+2y=36\begin{gather} 2x+y=24\\ x+2y=36 \end{gather}2x+y=24x+2y=36 If the solution is (x,y)(x,y)(x,y), enter in the va…
- Solve the system of equations using substitution. 381x+277y=3290701x−188y=2565\begin{gather} 381x+277y=3290\\ 701x-188y=2565 \end{gather}381x+277y=3290701x−188y=2565 If the so…
- Solve the system of equations using substitution. 8x−y−2z=27−x+2y+9z=162x−4y−2z=0\begin{gather} 8x-y-2z=27\\ -x+2y+9z=16\\ 2x-4y-2z=0 \end{gather}8x−y−2z=27−x+2y+9z=162x−4y−2z=0…
- Solve the system of equations using substitution. y+3x=3y+3x=3y+3x=3 2x+13y=52x+\frac{1}{3}y=52x+31y=5 The answer will be the solution for both variables.
- Adele built a rectangular wooden fence around her vegetable garden to keep the critters out. She used 505050 feet of fencing to surround the perimeter of the garden, and the gar…
- Alvin had three history tests during his first semester of his junior year of high school. The average of the first two exam scores was an 86;86;86; the average of the last two …
- If two triangles have all congruent angles and the triangles have the same perimeter, must they be congruent?
- Suppose ABCDABCDABCD is an isosceles trapezoid where AB‾∥CD‾\overline{AB} \parallel \overline{CD}AB∥CD and the angle measures in degrees are represented in terms of variables x,…
- Find xxx given the two equations: 3y−10=2x−10y+7x3=6\begin{align} 3y-10&=2x -10\\ y+\frac{7x}{3}&=6 \end{align}3y−10y+37x=2x−10=6