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You plan to solve this equation by substituting part of one equation into the other so you end up with an equation that contains only x's or only y's. the first thing you need to do in this procedure?
Wiki User
∙ 13y ago
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.
Wiki User
∙ 13y ago
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Solve this equation using substitution x equals y plus 6 and y equals -2-x?
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Why is an equation written in the form Ax plus By equals c called a linear equation?
The equation contains variables which are only raised to the first power.
How do you solve y equals x-3 and 2x equals y equals 3?
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.
What is the solution to x plus y equals 5 and 2x plus y equals 6?
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).
When does the nonlinear equation becomes linear equation?
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?
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.
Solve this equation using substitution x equals y plus 6 and y equals -2-x?
4
Why is an equation written in the form Ax plus By equals c called a linear equation?
The equation contains variables which are only raised to the first power.
How do you solve y equals x-3 and 2x equals y equals 3?
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.
How many ways can you solve this simultaneous equation x plus 2y equals 5 2x-y equals 15?
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.
The sum of two numbers is 36 the first number is three more than twice the second number find the larger number?
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.
What are the coordinates for y2x-10 yx-3?
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.
What is the solution to x plus y equals 5 and 2x plus y equals 6?
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).
When does the nonlinear equation becomes linear equation?
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.
What is mathematical induction?
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
Natasha and sonja drank 12 liters of water Natasha drank twice as much as sonja How many liters did Natasha drink?
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.
What is X plus 7y equals 33 and 3x - 2y equals 7?
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)
