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Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
3x + 4y = 38 → (1)
5x - 4y = - 30 → (2)
Since the coefficients of the y- term are opposites then adding the 2 equations will eliminate the term in y, that is
Add (1 ) and (2) term by term
(3x + 5x) + (4y - 4y) = (38 - 30), simplifying
8x = 8 ( divide both sides by 8 )
x = 1
The solution to the given system of equations is x = 1 and y = 8.75. In the elimination method, the basic operations are multiplication or division and addition or subtraction.
What are the steps in solving a system of linear equations by the elimination method?
The steps are as follows:
- Observe the equations for the same coefficients of any of the variables
- If they don't have the same coefficient then multiply or divide the coefficients of the equations to make them similar
- Add or subtract the equations from one another to eliminate one variable
- Simplify the equation in one variable to get its value
- Substitute that value in any of the equations to get the value of the other variable
Calculation:
The given system of linear equations:
3x + 4y = 38
5x - 4y = -30
Since both, the equations have same y-coefficient, adding both the equation to eliminate y- variable
⇒ 3x + 4y + 5x - 4y = 38 - 30
⇒ 8x = 8
∴ x = 1
Substituing x = 1 in first equation,
3(1) + 4y = 38
⇒ 3 + 4y = 38
⇒ 4y = 38 - 3
⇒ 4y = 35
⇒ y = 35/4
∴ y = 8.75
So, the solution of the given system of linear equations is (1, 8.75).
Learn more about solving a system of linear equations here:
https://brainly.com/question/13729904
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