To solve the system using a table, we'll first create a table and set up the equations:
Equation 1: 1-0.6x - 0.6y = -0.6
Equation 2: 10.5x-0.3y = -27
We'll start by selecting values for x and finding the corresponding y values for each equation. Let's choose x = 0, 1, and 2:
When x = 0:
Equation 1: 1-0.6(0) - 0.6y = -0.6
Simplifying, we get: 1 - 0 - 0.6y = -0.6
Simplifying further, we get: 1 - 0.6y = -0.6
Rearranging the equation, we get: 1 + 0.6y = -0.6
Subtracting 1 from both sides, we get: 0.6y = -1.6
Dividing both sides by 0.6, we get: y = -1.6/0.6 ≈ -2.67
Equation 2: 10.5(0) - 0.3y = -27
Simplifying, we get: -0.3y = -27
Dividing both sides by -0.3, we get: y = -27/-0.3 = 90
So, when x = 0, y ≈ -2.67 and y = 90.
When x = 1:
Equation 1: 1-0.6(1) - 0.6y = -0.6
Simplifying, we get: 1 - 0.6 - 0.6y = -0.6
Simplifying further, we get: 0.4 - 0.6y = -0.6
Rearranging the equation, we get: 0.4 + 0.6y = -0.6
Subtracting 0.4 from both sides, we get: 0.6y = -1
Dividing both sides by 0.6, we get: y = -1/0.6 ≈ -1.67
Equation 2: 10.5(1) - 0.3y = -27
Simplifying, we get: 10.5 - 0.3y = -27
Subtracting 10.5 from both sides, we get: -0.3y = -37.5
Dividing both sides by -0.3, we get: y = -37.5/-0.3 = 125
So, when x = 1, y ≈ -1.67 and y = 125.
When x = 2:
Equation 1: 1-0.6(2) - 0.6y = -0.6
Simplifying, we get: 1 - 1.2 - 0.6y = -0.6
Simplifying further, we get: -0.2 - 0.6y = -0.6
Rearranging the equation, we get: -0.2 + 0.6y = -0.6
Adding 0.2 to both sides, we get: 0.6y = -0.4
Dividing both sides by 0.6, we get: y = -0.4/0.6 ≈ -0.67
Equation 2: 10.5(2) - 0.3y = -27
Simplifying, we get: 21 - 0.3y = -27
Subtracting 21 from both sides, we get: -0.3y = -48
Dividing both sides by -0.3, we get: y = -48/-0.3 = 160
So, when x = 2, y ≈ -0.67 and y = 160.
Based on the values we calculated, the solutions to the system of equations are:
(x, y) ≈ (0, -2.67), (1, -1.67), (2, -0.67)
(x, y) = (0, 90), (1, 125), (2, 160)
Solve the system by using a table.
1-0.6x - 0.6y =-0.6
10.5x-0.3▶=-27
1 answer