Which of the following would be the best first step for solving the system of equations by elimination?
• 6.3x + 7.2y = 5.4
• 5.6x + 6.4y = 4.8
I would multiply the top eqn by 5.6 and the bottom one by 6.3
To solve the given system of equations by elimination, the best first step would be to either multiply one or both of the equations by a constant such that the coefficients of one of the variables in the two equations are equal in magnitude but opposite in sign. This will allow the terms with that variable to cancel out when the equations are added or subtracted.
To solve a system of equations by elimination, the goal is to eliminate one variable by manipulating the equations. In this case, we have the system of equations:
6.3x + 7.2y = 5.4
5.6x + 6.4y = 4.8
To begin, we need to choose a variable to eliminate. It's often helpful to choose the variable that will result in the simplest elimination process. Looking at the coefficients of x and y in both equations, we can see that they have a common multiple of 10.
So, let's start by multiplying the first equation by 10 and the second equation by -9 to make the coefficients of x equal:
(10)(6.3x + 7.2y) = (10)(5.4)
(-9)(5.6x + 6.4y) = (-9)(4.8)
This simplifies to:
63x + 72y = 54
-50.4x - 57.6y = -43.2
Now, we can add these two equations together in order to eliminate the x variable. Adding the equations gives:
63x - 50.4x + 72y - 57.6y = 54 - 43.2
Simplifying further:
12.6x + 14.4y = 10.8
Now, we've successfully eliminated the x variable. We can then proceed to solve the new equation using whatever method is appropriate (substitution, elimination, etc.).
So, the best first step for solving the given system of equations by elimination would be to multiply the first equation by 10 and the second equation by -9 in order to eliminate the x variable.