Question

Find the solution of the system of equations
-3x-2y=-4
9x+3y=15

Answer 1

The solution to the system of equations -3x-2y=-4 and 9x+3y=15 is found by using the elimination method, resulting in x = 2 and y = -1.

Step-by-step explanation:

The solution to the system of equations given by:

• -3x - 2y = -4
• 9x + 3y = 15

can be found using several methods, such as substitution or elimination. In this situation, the elimination method might be the simplest since the coefficients of x in both equations are multiples of each other. The steps are as follows:

1. Multiply the first equation by 3 to make the coefficients of x in both equations the same in magnitude but opposite in sign.
2. Add the modified first equation to the second equation to eliminate x.
3. Solve the resulting single-variable equation for y.
4. Substitute the value of y back into one of the original equations to solve for x.

Following these steps:

1. Multiply the first equation by 3:

• (-3x - 2y) * 3 = -4 * 3
• -9x - 6y = -12

Add the modified first equation to the second:

• -9x - 6y + 9x + 3y = -12 + 15
• -3y = 3

Divide by -3 to solve for y:

• y = -1

Substitute y = -1 into the second original equation:

• 9x + 3(-1) = 15
• 9x - 3 = 15
• Add 3 to both sides:
• 9x = 18
• Divide by 9:
• x = 2

The solution to the system of equations is x = 2 and y = -1.

Answer 2

Answer: x = 2, y = -1

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