Substitution method :
The equations are
---------------->(1)
---------------->(2)
Solve for y.
---------------->(3)
Substitute the values in (1).
.
Substitute the values in (3).
.
The solution of the system is and .
System of Linear Equations entered :
[1] 3x - 2y = 14 [2] 5x - y = 32Graphic Representation of the Equations :
-2y + 3x = 14 y + 5x = 32Solve by Substitution :
// Solve equation [2] for the variable y
// Plug this in for variable y in equation [1]
// Solve equation [1] for the variable x
[1] 7x = 50 [1] x = 50/7// By now we know this much :
x = 50/7 y = 5x-32// Use the x value to solve for y
Solution :
{x,y} = {50/7,26/7}System of Linear Equations entered :
[1] 3x - 2y = 14 [2] 5x + y = 32Graphic Representation of the Equations :
-2y + 3x = 14 y + 5x = 32Solve by Substitution :
// Solve equation [2] for the variable y
// Plug this in for variable y in equation [1]
// Solve equation [1] for the variable x
[1] 13x = 78 [1] x = 6// By now we know this much :
x = 6 y = -5x+32// Use the x value to solve for y
Solution :
{x,y} = {6,2}How do you find the solution to a system of linear equations?
How do I solve systems of linear equations by substitution?.
Isolate one of the two variables in one of the equations..
Substitute the expression that is equal to the isolated variable from Step 1 into the other equation. ... .
Solve the linear equation for the remaining variable..
What is the solution to the system of equations y =
Summary: The solution to the system of equations y = -5x + 3 and y = 1 is x = 0.4 and y = 1.
How many solutions does this linear system have Y 5x 1 15x 3y 3?
Summary: If y = 5x - 1 and -15x - 3y = 3, the solution of the linear equations is (0, -1) i.e., one solution.
What are the 3 solutions to systems of equations?
There are three methods used to solve systems of equations: graphing, substitution, and elimination. To solve a system by graphing, you simply graph the given equations and find the point(s) where they all intersect.