Question

Solve by Elimination

3 + 2x - y = 0
-3 - 7y = 10x

X = ?
y = ?
A) X = -3, y = 2
B) X = 3, y = -2
C) X = 2, y = -3
D) X = -2, y = 3

Answer 1

The system of equations provided does not have a solution that matches the given options. Through elimination, the solution calculated is x = -0.75 and y = 1.5, indicating a potential error in the original question or provided options.

Step-by-step explanation:

The student asks to solve a system of equations by elimination. The two equations given are:

1. 3 + 2x - y = 0 (Equation 1)
2. -3 - 7y = 10x (Equation 2)

To use elimination, we want to align these equations in such a way that one of the variables will be eliminated when we add or subtract the equations from each other. First, let’s arrange both equations in standard form, aligning the terms with x and y, and the constants:

1. 2x - y = -3 (Equation 1 rearranged)
2. 10x + 7y = 3 (Equation 2 rearranged)

Now, we need to multiply Equation 1 by 10 and Equation 2 by 2 so that the x terms will have the same coefficient:

1. 20x - 10y = -30 (Equation 1 multiplied by 10)
2. 20x + 14y = 6 (Equation 2 multiplied by 2)

Subtracting the second equation from the first gives us:

1. -24y = -36

Dividing by -24 to solve for y we get:

1. y = 1.5

Substituting y = 1.5 into Equation 1 (2x - y = -3), and solving for x:

1. 2x - 1.5 = -3
2. 2x = -1.5

Dividing by 2 to solve for x:

1. x = -0.75

The solution is x = -0.75 and y = 1.5, which is not one of the options provided in the question. There must be an error in the options provided or in the original equations.