Question

Solve the system of linear equations. 0.3x-0.2y=-2.1 0.6x 1.3y=0.9

Answer 1

To solve the given system of linear equations, use the elimination method. Multiply the first equation by 2 and then subtract it from the second one to find y = 3. Substitute y back into the first equation to solve for x, which results in x = -5.

Step-by-step explanation:

Solving a System of Linear Equations

To solve the system of linear equations given by 0.3x-0.2y=-2.1 and 0.6x+1.3y=0.9, you can use the method of substitution or elimination. Let's use elimination in this instance. First, simplify the equations if needed. In this case, the equations are already simplified and ready to use.

Step 1: Multiply the first equation by 2 to get rid of decimals:

• 2*(0.3x - 0.2y) = 2*(-2.1)
• 0.6x - 0.4y = -4.2

Step 2: Now, subtract the first equation from the second:

• 0.6x + 1.3y - (0.6x - 0.4y) = 0.9 - (-4.2)
• 1.7y = 5.1

Step 3: Divide by 1.7 to isolate y:

• y = 5.1 / 1.7
• y = 3

Step 4: Now substitute y = 3 into one of the original equations to find x. We'll use the first equation for this:

• 0.3x - 0.2(3) = -2.1
• 0.3x - 0.6 = -2.1
• 0.3x = -1.5
• x = -1.5 / 0.3
• x = -5

Therefore, the solution to the system is x = -5 and y = 3.