Solving by graphing DQ 1
Solving by substitution
Solving by elimination
Which method do you think would be best to solve this system?
y=10x-8
y=1/2x+5
y = 10x - 8
Multiply both sides of second equation by 20.
20y = 10x + 100
Subtract first equation from second.
19y = 108
To determine the best method for solving the given system of equations, it is helpful to consider the strengths and weaknesses of each method.
1. Solving by graphing:
This method involves graphing the equations on a coordinate plane and determining the point where the two lines intersect. While it can be useful for visualizing the solution, it can sometimes be challenging to pinpoint the exact coordinates of the intersection point. Additionally, it may not be the most efficient method if the solution is not easily identifiable.
2. Solving by substitution:
This method involves solving one equation for a variable and then substituting that expression into the other equation. It can be advantageous when one equation can be easily solved for a variable, which makes it straightforward to substitute into the other equation. However, if the equations are complex, substitution might lead to difficult calculations.
3. Solving by elimination:
This method involves adding or subtracting the equations in a way that cancels out one of the variables, allowing for the determination of the other variable. Elimination is often preferred when the coefficients of one variable in both equations are already the same or can be made the same easily. It can be efficient and straightforward, especially when dealing with linear equations.
Considering the given system of equations:
y = 10x - 8
y = (1/2)x + 5
Based on the simplicity of the coefficients, the method of elimination is likely the most straightforward and efficient approach for solving this system. The equations have different coefficients for both x and y, making substitution more difficult. Graphing can be helpful for visualizing the solution, but may not provide an exact solution in this case. By using the elimination method, we can manipulate the equations to eliminate one variable and solve for the other.