Elimination by Addition and Subtraction - Examples & Practice
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- (Video) The Elimination Method: Adding by ThinkwellVids (Video) The Elimination Method: Subtracting by ThinkwellVids These videos by ThinkwellVids cover elimination through addi…
By Alex Federspiel, Zora Gilbert, Christine, Amy Feraco, Caroline K, Jonathan Heller, Anusha Rahman
- Add or Subtract for Elimination in Systems of Linear Equations Earlier we saw how to solve a system of linear equations via grouping and via substitution. The main idea of the e…
By Stefan Cuevas, Alex Federspiel, Sarah Walker, Joshua Siktar, Caroline K, Anusha Rahman
- Add or Subtract for Elimination in Systems of Linear Equations Here is a graphic with an example of how to ADD terms in a system of equations in order to eliminate the terms wit…
By Caroline K
Problems 28
- Suppose that (x,y)(x,y)(x,y) is the solution to the following system of equations. −7y−4x=1-7y-4x=1−7y−4x=1 7y−2x=537y-2x=537y−2x=53 Find yyy.
- Solve the following system for (x,y)(x,y)(x,y). −14y−8x=2-14y-8x=2−14y−8x=2 14y−4x=10614y-4x=10614y−4x=106
- Solve the system of equations using addition or subtraction. 3x+2y=113x+2y=113x+2y=11 x+2y=7x+2y=7x+2y=7
- If x,yx,yx,y are real numbers such that 4x+3100y=104x+3^{100}y=104x+3100y=10 and x−3100y=5x-3^{100}y=5x−3100y=5, find xxx. (Hint: Solve using addition or subtraction.)
- Solve the system. x−y=83y−x=12\begin{align} x-y&=8\\ 3y-x&=12 \end{align}x−y3y−x=8=12
- If α\alphaα is a real variable, solve for xxx and yyy in terms of α\alphaα. 2x+αy=22x+\alpha y=22x+αy=2 2x+(α−1)y=−22x+(\alpha-1)y=-22x+(α−1)y=−2
- Solve for xxx and yyy in terms of the nonzero variables α\alphaα and β\betaβ. αx+2βy=7\alpha x + 2\beta y=7αx+2βy=7 3αx−2βy=53\alpha x - 2\beta y = 53αx−2βy=5
- Suppose that a quadratic function f(x)=x2+bx+cf(x) = x^2 + bx + cf(x)=x2+bx+c passes through the points (1,2)(1,2)(1,2) and (3,2)(3,2)(3,2). What is the value of ccc?
- Let △ABC\triangle ABC△ABC be a triangle with AB=3AB = 3AB=3, BC=4BC = 4BC=4, and AC=5AC = 5AC=5. Let III be the center of the circle inscribed in △ABC\triangle ABC△ABC. What is …
- Solve the following system of equations: −3x+9y=−152x−6y=46\begin{align} -3x + 9y &= -15 \\ 2x - 6y &= 46 \end{align}−3x+9y2x−6y=−15=46
- A motorboat travels 486486486 km in 999 hours going upstream and 470470470 km in 555 hours going downstream. What is the speed of the boat in still water, and what is the speed …
- Which variable(s) are easiest to eliminate when we solve systems of linear equations using elimination?
- Which of the following is not a step in solving the following system of linear equations using elimination? x−2y=8x - 2y = 8x−2y=8 −x+3y=4-x + 3y = 4−x+3y=4
- What is the solution to the following system of linear equations? 2x+y=142x + y = 142x+y=14 2x+8y=02x + 8y = 02x+8y=0
- If a+b=4a+b=4a+b=4 and a−b=2a-b=2a−b=2, what is 2ab2ab2ab?
- At the end of the week, you made a total of 80.00\80.0080.00 and sold a total of 888888 glasses of lemonade and ice cream sandwiches combined. Which item sold more?
- You and a friend go to a fast food Mexican grill. You order 333 burritos and 111 soft taco. Your bill totals 12.75\12.7512.75. Your friend's bill is 11.50\11.5011.50 for only 11…
- You are shopping for a new phone plan. One network offers a plan with a cost of C=0.25d+5C = 0.25d + 5C=0.25d+5 where ddd is how many GB of data you use. Another network offers …
- Justin just graduated from college and is deciding which job offer to take. He plans to work hhh hours per month. After his monthly spending, he is left with sss dollars left ov…
- Is there a solution for this system of linear equations? 2y=4x+64y=4x+12\begin{array}{rcl} 2y&=&4x+6 \\ 4y&=&4x+12 \end{array}2y4y==4x+64x+12
- Consider the graph above. What is the xxx-coordinate of the purple point?
- Consider the graph above. What is the yyy-coordinate of the purple point?
- Consider the graph above. What are the coordinates of the purple point?
- Consider the graph above. What are the coordinates of the purple point?
- Solve the following system of equations: 2x+3y=132x + 3y = 132x+3y=13 −5x+2y=−4-5x + 2y = -4−5x+2y=−4 3x−2y=03x - 2y = 03x−2y=0
- Cassandra had two exams in her math class, with an average score of 858585, and the difference in the scores of the two exams being 202020. What was the larger of the two exam s…
- A triangle has three sides of lengths A,B,A, B,A,B, and CCC. The sum of the lengths of the two shortest sides is 161616, and the triangle's semiperimeter is 141414. What is the …
- If a parabola passes through the points (2,0)(2, 0)(2,0) and (3,1),(3, 1),(3,1), how many possible locations are there for the vertex of the parabola?