This is the substitution technique of solving a system of equations. It is carried out as follows:
1. Choose one of the two equations you have & rewrite it to define the value of only one variable(either x or y ).
2. substitute the value of the variable you chose in the first step into the other equation.
3. You'll obtain one equation in terms of one variable so you can solve for it.
4. Substitute the value of the variable you found in the third step into any one of the original two equations of the question, this way you'll solve for the other variable.
5. To check the correctness of your solution, you can substitute the values of the two variables into the two equations you originally have, if the two mathematical equalities you'll have are correct then your answer is also correct.
Example:
Solve the following system of equations to find both x & y:
x + y = 3
-x + 2y = 0
Solution:
choose the first equation & rewrite it:
x = 3 - y
substitute the value of x into the second equation:
- (3- y) + 2y = 0
-3 +y + 2y = 0
-3 + 3y = 0
3y = 3
y = 1
Substitute the value of y into any of the 2 original equations, say the first:
x + 1 = 3
x = 2
Hope this will help.
4
The equation contains variables which are only raised to the first power.
The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.
Given: x + y = 5 2x + y = 6 We can subtract the second equation from the first to get: -x = -1 x = 1. From there, substituting back in to the first equation yields: 1 + y = 5 y = 4. The solution is (1, 4).
A linear equation is defined as an equation that contains only the first power of the unknown quantity. For example, 5x - 3 = 7 where "x" is the unknown quantity is a linear equation. If an equation contains an unknown quantity having a higher power than 1, then the equation ceases to be a linear equation. For example, 3x2 + 5x + 7 = 0 is a non linear equation known as a quadratic equation, because the unknown quantity "x" has a power of 2. Similarly, equations containing unknowns with higher powers such as x3, x7, x12 are all non linear equations.
If r = 5z, then 15z = 3y, then r = y. This can be solved easily by solving for z in the second equation and substituting into the first equation.
4
The equation contains variables which are only raised to the first power.
The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.The second "equation" is, in fact, two equations, and the three equations are inconsistent.The "second" equation gives :2x = 3 so that x = 3/2 and also y = 3But substituting these values in the first equation implies that 3 = (3/2) - 3or 3 = 3/2 or 2 = 1 which is a contradiction.
This system has the unique solution (7, -1). Solving the first equation for x and substituting gives us y = -1; substituting that into either of the original equations gives x = 7. You can see the steps in between using the link in the "related links" section below.
25+11=36: Let f and s represent the first and second numbers respectively. The statement of the problem yields two equations: f + s =36 and f = 3 + 2s. Substituting the function given in the second equation for f into the first equation yields 3 + 2s + s = 36, or (subtracting 3 from each side and merging the s terms, 3s = 33 or s = 11. Then f + 11 = 36 (substituting the value for s into the first equation), or f = 25.
Unfortunately, the browser used by Answers.com for posting questions is incapable of accepting mathematical symbols. I'll guess the question you are asking is: What is the common point of the two lines y = 2x - 10 and y = x - 3? The common point where they cross is (7, 4) Substituting for y in the first equation by x - 3 as given by the second equation gives: x - 3 = 2x - 10 → x = 7 The substituting in the first equation gives y = 2 x 7 - 10 = 4 Checking in the second: y = 7 - 3 = 4 as expected.
Given: x + y = 5 2x + y = 6 We can subtract the second equation from the first to get: -x = -1 x = 1. From there, substituting back in to the first equation yields: 1 + y = 5 y = 4. The solution is (1, 4).
Mathematical Induction is a process uses in College Algebra It can be used to prove that a sequence is equal to an equation For Example: 1+3+5+7+n+2=2n+1 there are 3 steps to mathematical induction the first includes proving that the equation is true for n=1 the second includes substituting k for every n-term the third involves substituting k+1 for every k-term to prove that both sides are equal
A linear equation is defined as an equation that contains only the first power of the unknown quantity. For example, 5x - 3 = 7 where "x" is the unknown quantity is a linear equation. If an equation contains an unknown quantity having a higher power than 1, then the equation ceases to be a linear equation. For example, 3x2 + 5x + 7 = 0 is a non linear equation known as a quadratic equation, because the unknown quantity "x" has a power of 2. Similarly, equations containing unknowns with higher powers such as x3, x7, x12 are all non linear equations.
Natasha drank 8 liters and Sonja drank 4.8 is twice as much as 4, and 8+4=12. Or, using algebra: n= 2 * s and s + n = 12. Substituting from the first equation into the second, s + 2 * s = 12, or 3 * s = 12, therefore s = 12 / 3 = 4 and (substituting the value of s into the first equation, n = 2 * 4 = 8.
x + 7y = 33 multiply through by 3: 3x + 21y = 99 Subtract the second equation from the above equation: 23y = 92 So y = 4 Substituting this value of y in the first equation, x + 28 = 33 ie x = 5 The solution is (x,y) = (5,4)