fan+ medal 2. A system of equations is given below. 2x + 7y = 1 -3x – 4y = 5 a. Create an equivalent system of equations by replacing the first equation by multiplying the first equation by an integer other than 1, and adding it to the second equation. b. Use any method to solve the equivalent system of equations (the new first equation with the original second equation). c. Prove that the solution for the equivalent system is the same as the solution for the original system of equations.
a) an integer can be negative, zero or positive choose a number but not 1 and multiply each term of equation 1 and adding it to the second equation? this just tells me I have a system of equations. new equation 1 + original equation 2 b) solve the system of equations There are 3 main ways to solve simultaneous equations 1 by graphing 2 by substitution and 3 by elimination. Do you need help to solve the equation? c)To prove that the solution for the equivalent system is the same as the solution for the original system of equations substitute the values for x and y in the original equations and compute each side separately. If the right hand side = left hand side then the solution is the same.
I would use substitution to solve this one.
oh I forgot method #4 using matrices. you can tell I didn't use it very often.
- multiply the first original equation by 3 . -then add the resulting first equation with the second original equation. -u will get a new equation ,again add the new equation to the second original equation , the x variable will be cancelled and u will get the value of y. -now put the value of y in any of the original equations to get the value of x. -now put the value of both x and y on the LHS (LEFT HAND SIDE)in any of the original equation. compare the value obtained in the LHS AND RHS ,if the LHS=RHS then your answer is correct.
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