Julie is asked to solve the system below by elimination. Which of the following steps would be the best way to begin?
i. 2x+y=−3
ii. 3x−2y=2
To solve the system by elimination, we want to eliminate one of the variables by adding or subtracting the equations. The best way to begin is to multiply the first equation by 3 and the second equation by 2 so that the coefficients of the x terms will be the same. Therefore, the best way to begin is to perform the following step:
i. Multiply the first equation by 3:
3(2x + y) = 3(-3)
6x + 3y = -9
ii. Multiply the second equation by 2:
2(3x - 2y) = 2(2)
6x - 4y = 4
Now, the coefficients of the x terms are the same, and we can proceed with eliminating the x term.
To solve the system of equations by elimination, you want to eliminate one variable by adding or subtracting the two equations. In this case, it is best to eliminate the x variable or the y variable.
To begin, you need to select one of the variables to eliminate. Let's choose to eliminate the x variable.
Multiply equation (ii) by 2 to make the coefficients of x the same:
2(3x - 2y) = 2(2)
This simplifies to:
6x - 4y = 4
Now that the coefficients of x are the same, we can add equation (i) and the new equation we just obtained:
2x + y = -3
6x - 4y = 4
After adding these two equations, we can proceed to solve for one of the variables using the resulting equation.
To solve the system of equations by elimination, you need to eliminate one of the variables so that you're left with an equation involving only one variable. This can be accomplished by manipulating the equations in a way that will cause a variable to cancel out when you add or subtract the equations.
In this case, let's choose to eliminate the variable "y". To do this, we can multiply equation i by 2 and equation ii by 1, so that the coefficients of "y" in both equations have opposite signs:
i. 2(2x + y) = 2(-3) -> 4x + 2y = -6
ii. 1(3x - 2y) = 1(2) -> 3x - 2y = 2
Now, if we add the two equations together, the "y" terms will cancel out:
(4x + 2y) + (3x - 2y) = -6 + 2
4x + 3x + 2y - 2y = -4
7x = -4
The next step would be to solve for "x" by dividing both sides of the equation by 7:
7x/7 = -4/7
x = -4/7
So, the best way to begin solving this system by elimination would be to multiply equation i by 2 and equation ii by 1.