What are the steps to doing y = mx + b case for system of linear equations?
What is your system?
Well there are about 2 systems that follows the one I am currently stuck on.
Y= 0.3x -2 = 1.5x -0.4
We have to find the x and y pair that satisfies the system - of linear equations.
(over all) finding the intersection of those 2 equations.
To solve a system of linear equations in the form of y = mx + b, you can follow these steps:
Step 1: Write down the given equations:
- Let the first equation be y = m₁x + b₁.
- Let the second equation be y = m₂x + b₂.
Step 2: Set the two equations equal to each other:
- Equate the right-hand sides of the equations: m₁x + b₁ = m₂x + b₂.
Step 3: Collect all the x-terms on one side of the equation and the constants on the other side:
- Subtract m₂x from both sides of the equation: m₁x - m₂x + b₁ = b₂.
Step 4: Simplify the equation by combining like terms:
- Combine the x-terms: (m₁ - m₂)x + b₁ = b₂.
Step 5: Solve for x:
- Subtract b₁ from both sides of the equation: (m₁ - m₂)x = b₂ - b₁.
- Divide both sides of the equation by (m₁ - m₂): x = (b₂ - b₁) / (m₁ - m₂).
Step 6: Substitute the x-value back into either of the original equations to find the corresponding y-value:
- Use the equation y = mx + b and replace x with the found value in Step 5: y = m₁ * [(b₂ - b₁) / (m₁ - m₂)] + b₁.
- Simplify the equation to get the value of y.
Step 7: Express the solution as an ordered pair (x, y) if required.
Therefore, by following these steps, you can solve a system of linear equations in the form of y = mx + b.