A system of equations is a set of two or more equations with the same variables. The solution to a system of equations is the point where the graphs of the equations intersect.
First, solve one equation for one variable and substitute it into the other equation.
Next, add or subtract the equations to eliminate one variable, then solve for the remaining variable.
Finally, graph both equations and find the point where they intersect, which is the solution to the system.
Solve the system of equations:
1) 2x + 3y = 6 2) x - y = 1
Solution (Substitution Method):
Step 1: Solve the second equation for x.
x = y + 1
Step 2: Substitute x = y + 1 into the first equation.
2(y + 1) + 3y = 6
2y + 2 + 3y = 6
5y = 4
y = 4/5
Step 3: Substitute y = 4/5 into x = y + 1 to find x.
x = 4/5 + 1
x = 9/5
Solve the system of equations:
1) 3x + 4y = 12 2) 2x - 4y = 4
Solution (Elimination Method):
Step 1: Add the two equations to eliminate y.
(3x + 4y) + (2x - 4y) = 12 + 4
5x = 16
x = 16 / 5
Step 2: Substitute x = 16/5 into one of the original equations.
3(16/5) + 4y = 12
48/5 + 4y = 12
4y = 12 - 48/5
4y = 60/5 - 48/5
4y = 12/5
y = 3/5
Graph the system of equations:
1) y = 2x + 1 2) y = -x + 4
Solution (Graphing Method):
Plot both equations on a graph and find the point where they intersect. The intersection point is the solution to the system.
For this system, the graphs intersect at (1, 3).
Now, try solving this system of equations:
1) 4x + 2y = 8 2) 3x - y = 3Click here for the solution