Substitution Method — Definition & Examples
Read this topicExplanations 3
- Swap them out! When you have a problem with at least one variable, you can swap the variable out with a number in order to learn more about the problem. For example, take the ex…
By Zora Gilbert, Alex Federspiel, Victor Wang, Christine, Joshua Siktar, Jonathan Heller
- (Video) Evaluating Variable Expressions by mathman1024 Here's a video by mathman1024 that shows you how to evaluate variable expressions. Summary\large{\text{Summary}}Summary Le…
By Alex Federspiel, Jonathan Heller, Caroline K, Joshua Siktar
- Substituting for a Variable Let's say you have an expression with a variable in it. If you know the value that the variable is equal to, you can substitute that value in for the…
By Caroline K, Alex Federspiel, Joshua Siktar
Problems 61
- If x=2x=2x=2 and y=−4y=-4y=−4, find the values of 3xy23xy^23xy2 and 2x−3y2x-3y2x−3y, in that order.
- Find the values of −b−b2−4ac2a\frac{-b - \sqrt{b^2-4ac}}{2a}2a−b−b2−4ac and −b+b2−4ac2a\frac{-b + \sqrt{b^2-4ac}}{2a}2a−b+b2−4ac if a=1a=1a=1, b=−5b=-5b=−5, and c=4ac=4ac=4a.
- If x=2yx=2yx=2y, y=12 zy=\frac{1}{2}\ zy=21 z, and z=4z=4z=4, find the value of 6xy+3z−4yz.6xy+3z-4yz.6xy+3z−4yz.
- If x=10x=10x=10, find the value of 3x+123x+123x+12.
- If a=4a=4a=4 and b=−4b=-4b=−4, compute the value of 4−ab +4ab2.4-\frac{a}{b}\ +4ab^2.4−ba +4ab2.
- If xy=32\frac xy = \frac32yx=23 and yz=57\frac yz = \frac57zy=75, what is zx\frac zxxz?
- If x=4,y=5,x=4, y=5,x=4,y=5, and z=7z=7z=7 then what is the value of 2x+4y−z2x +4y -z2x+4y−z?
- If x,yx,yx,y are real numbers with product xy=1xy = 1xy=1, find the maximum possible value of the sum 11+x+11+y\frac{1}{1+x} + \frac{1}{1+y}1+x1+1+y1.
- Simplify the expression 4+x4+x4+x when x=5x=5x=5.
- Simplify the expression 18−x18-x18−x when x=−3x=-3x=−3.
- Simplify the expression 2x−142x-142x−14 when x=8x=8x=8.
- Simplify the expression A+A+B+C+D+EA+A+B+C+D+EA+A+B+C+D+E when A=1B=A+AC=B+AD=C+Band E=D+C\begin{align} A&=1\\ B&=A+A\\ C&=B+A\\ D&=C+B\\ \text{and }E&=D+C \end{align}ABCDand E…
- Let a=1314a=\sqrt{\frac{13}{14}}a=1413. What is 121−a+121+a\frac{12}{1-a}+\frac{12}{1+a}1−a12+1+a12? Source: inspired by AIME 2016
- Given that a=−3a = -3a=−3, which is the largest value in the following list? 1,−a,2a,a2,5−2a\begin{array}{ccc} 1,& -a,& \frac{2}{a},& a^2,& 5-2a \end{array}1,−a,a2,a2,5−2a
- We can define the remainder for real numbers xxx and yyy (with y≠0y \not= 0y=0) by rem(x,y)=x−y⌊xy⌋\text{rem}(x,y) = x - y \left\lfloor \frac{x}{y} \right\rfloorrem(x,y)=x−y⌊y…
- Suppose that x+y=2x+y=2x+y=2 and y+2=3y+2=3y+2=3. Does x=yx=yx=y?
- If a=1a = 1a=1 and b=3b = 3b=3, then b+a= ?b+a =\,?b+a=?
- If x=3x=3x=3, y=4y=4y=4, and z=5z=5z=5, then what does 2z+y+3x2z+y+3x2z+y+3x equal?
- If a=ba=ba=b and a−c=x−ca-c=x-ca−c=x−c, then what is xxx?
- Simplify completely: 4x5⋅34x2\frac{4x}{5}\cdot\frac{3}{4x^2}54x⋅4x23
- If a=2a=2a=2 and b=−1b=-1b=−1, what is the value of a+ab +b2a+\frac{a}{b}\ +b^2a+ba +b2
- If a=5a=5a=5 and b=−10b=-10b=−10, what is the value of a2+2ab+b2?a^2+2ab+b^2?a2+2ab+b2?
- If a=2a=2a=2 and b=−1b=-1b=−1, what is the value of (a+b)(a2−ab+b2)?(a+b)(a^2-ab+b^2)?(a+b)(a2−ab+b2)?
- If a=−35a=-35a=−35 and b=7b=7b=7, what is the value of a×b+ab?a\times b+\frac{a}{b}?a×b+ba?
- If a=100a=100a=100 and b=−10b=-10b=−10, what is the value of −ab+b2a?\frac{-a}{b}+\frac{b^2}{a}?b−a+ab2?
- If a=2a=2a=2, b=−1b=-1b=−1, and c=1c=1c=1, what is the value of a×b+a×cb +b2?a\times b+\frac{a\times c}{b}\ + b^2?a×b+ba×c +b2?
- What number should you set your laser to?
- Simplify the fraction 12−x−x\frac{12-x}{-x}−x12−x when x=2x=2x=2.
- Simplify the expression x+(y)(z)x + (y)(z)x+(y)(z) when x=1,y=2x,z=−12yx=1,\quad y=2x,\quad z=-\frac{1}{2}yx=1,y=2x,z=−21y
- Simplify the expression 2x+y2^{x+y}2x+y when x=1x=1x=1 and y=3y=3y=3.
- Simplify the expression 9x9x9x when x=13x=\frac{1}{3}x=31.
- The cost of renting a car from a popular car rental company is 500\500500, plus another 0.10\0.100.10 per mile driven. If you rent a car and drive from Pittsburgh to Philadelphi…
- Simplify the expression 43−x4^{3-x}43−x when x=1x=1x=1.
- If xxx is a factor of yyy and yyy is a factor of xxx, which of the following is true?
- If a number xxx is a factor of another number yyy, what is the greatest common factor of xxx and yyy? Note: both xxx and yyy are greater than 1.1.1.
- What is xxx in the equation x−y=3x-y=3x−y=3 when y=2y=2y=2?
- Simplify the expression x+2x + 2x+2 when x=3x=3x=3.
- Let aaa and bbb be positive numbers where a<ba<ba<b. Suppose a−b=ca-b=ca−b=c. Is ccc positive or negative?
- Evaluate 3x+93x+93x+9 when x=7x=7x=7.
- Simplify x+9x+9x+9, given y=11y=11y=11.
- Evaluate x(x(x+1)+1)+1x(x(x+1)+1)+1x(x(x+1)+1)+1 when x=2x=2x=2.
- Evaluate 8+(−x)8+(-x)8+(−x) when x=−5x=-5x=−5.
- True or False\text{True or False}True or False === If m>n>0m>n>0m>n>0 then 1m>1n\frac1m>\frac1nm1>n1.
- If y=2x+3y = 2x+3y=2x+3, then 2y=?2y ={?}2y=?
- Solve for XXX when A=38135A=\frac{38}{135}A=13538, L=14L=\frac14L=41, and E=13538E=\frac{135}{38}E=38135.
- We have a literal equation: 4x+3y=364x+3y = 364x+3y=36 We also know the relationship between xxx and yyy, it is: y=x+1y=x+1y=x+1 Is there a way to re-write the original literal …
- We have the following equation: a+(b×c)=da+(b\times c) =da+(b×c)=d When a=2,c=3,d=23a=2, c=3, d=23a=2,c=3,d=23, what is the value of bbb?
- We have a function: y=−2x+5y=-2x + 5y=−2x+5 Which of the following values of xxx will yield the biggest yyy?
- What is the value of the expression x2y+y2xx^2y+y^2xx2y+y2x when x=2x= 2x=2 and y=10y=10y=10?
- When x=5x=5x=5 and y=−2y=-2y=−2, which of the following expressions is the biggest?
- True or False\text{True or False}True or False === No matter what numbers you put in for aaa and bbb, the product of −a×−b-a\times -b−a×−b will always be positive.
- What value below makes the expression undefined? x+88−x\frac{x+8}{8-x}8−xx+8
- Select the values of xxx that make the equation true. x×0=xx\times0=xx×0=x
- Consider the expression: 4x−2x+x4x-2x+x4x−2x+x Which value of xxx gives the largest value of this expression?
- What is the value of the following expression when x=82x=82x=82? (7,827+8,884+2,946+3,209+1,225)×(3x−246)×(x2−79)(7{,}827+8{,}884+2{,}946+3{,}209+1{,}225)\times(3x-246)\times(x^…
- Simplify the expression A+B+C+D+EA+B+C+D+EA+B+C+D+E when A=1B=2C=3D=4and E=5\begin{align} A&=1\\ B&=2\\ C&=3\\ D&=4\\ \text{and }E&=5 \end{align}ABCDand E=1=2=3=4=5
- Simplify the expression A−B+C−DA-B+C-DA−B+C−D when A=1B=3AC=2BD=A+C\begin{align} A&=1\\ B&=3A\\ C&=2B\\ D&=A+C \end{align}ABCD=1=3A=2B=A+C
- Simplify the expression A−B−C−D−EA-B-C-D-EA−B−C−D−E when A=100B=AC=5BD=ACand E=D4+DA=100\quad\quad B=\sqrt{A}\\ C=5B\quad\quad D=\frac{A}{C}\\\text{and }E=D^4+DA=100B=AC=5BD=CA…
- Simplify the expression A+B−C+D−EA+B-C+D-EA+B−C+D−E when A=1B=A+AC=A×AD=AAand E=A−BC+D\begin{align} A&=1\\ B&=A+A\\ C&=A\times A\\ D&=A^A\\ \text{and }E&=A-\frac{B}{C+D} \end{al…
- Which of the following expressions are equivalent to x−yx-yx−y?
- Which of the following are fraction decompositions of a+b+cd\frac{a+b+c}{d}da+b+c?