Use addition to solve the linear system of equations.
{Y=-3x+1
{Y=2x-4
(-2,1)
(1,-2)
(1,2)
(-1,-2)
(1,-2)
To solve the linear system of equations using addition, we need to eliminate one variable by adding the two equations together. Let's start solving the system step-by-step.
Given equations:
1) Y = -3x + 1
2) Y = 2x - 4
To eliminate the variable Y, we will add both equations together.
Step 1: Add the equations
(-3x + 1) + (2x - 4)
Step 2: Simplify the equation
-3x + 1 + 2x - 4
Step 3: Combine like terms
(-3x + 2x) + (1 - 4)
-x - 3
Now we have a new equation -x - 3, which represents the relationship between x and Y. Let's solve for x.
Step 4: Solve for x
-x - 3 = 0
Step 5: Add x to both sides
-x + x - 3 = 0 + x
-3 = x
Now, we have found the value of x, which is x = -3.
Step 6: Substitute the value of x into one of the original equations to find the value of Y.
Using equation 1) Y = -3x + 1:
Y = -3(-3) + 1
Y = 9 + 1
Y = 10
Therefore, the solution to the linear system of equations is x = -3 and Y = 10.
To solve a linear system of equations by addition, follow these steps:
Step 1: Write down the equations in the system.
Equation 1: Y = -3x + 1
Equation 2: Y = 2x - 4
Step 2: Set the two equations equal to each other.
-3x + 1 = 2x - 4
Step 3: Rearrange the equation to isolate x.
Add 3x to both sides: -3x + 3x + 1 = 2x + 3x - 4
Simplify: 1 = 5x - 4
Add 4 to both sides: 1 + 4 = 5x - 4 + 4
Simplify: 5 = 5x
Divide both sides by 5: 5/5 = 5x/5
Simplify: 1 = x
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Using Equation 1: Y = -3(1) + 1
Simplify: Y = -3 + 1
Y = -2
Therefore, the solution to the linear system of equations is (x, y) = (1, -2).
To check if the other given points (-2, 1), (1, -2), (1, 2), and (-1, -2) are solutions to the system of equations, substitute the x and y values into both equations. If the equations are true, then the points are valid solutions.