I have learned that we can solve a system of two equations with two unknowns in three different ways. I'm going to explain how to solve two equations with three different methods.
Substitution method
You are given two equations:
2x+y=4
3x+2y=1
First you have to solve the equation for y in terms of x.
2x+y=4
y=4-2x
Then you have to use the other equation to solve the x in terms of y.After that you can fill in what you found out y equals, and then solve the equation.
3x+2y=1
3x=1-2y
3x=1-2(4-2x)
3x=1-8+4x
3x-4x=-7
-x=-7 |:(-1)
x=7
Next you have to find y, by putting 7 in for x.
y=4-2(7)
y=4-14
y=-10
The solution is (7,-10)
Elimination method
You are given two equations:
4x-y=16
3x-y=10
First you have to subtract 4x and 3x, and then you have to subtract -y and -y, and subtract 16 and 10. Then you have:
x=6
Now you have to find y, by substituting 6 for x in either original equation.
3(6)-y=10
18-y=10
y=18-10
y=8
The solution is (6,8)
Graphing method
On this method you can make a graph, and make the lines from the two given equations. For example you can use desmos.com. Then you just have to look at the exact coordinates of the point where the lines intersect from the graph.
Substitution method
You are given two equations:
2x+y=4
3x+2y=1
First you have to solve the equation for y in terms of x.
2x+y=4
y=4-2x
Then you have to use the other equation to solve the x in terms of y.After that you can fill in what you found out y equals, and then solve the equation.
3x+2y=1
3x=1-2y
3x=1-2(4-2x)
3x=1-8+4x
3x-4x=-7
-x=-7 |:(-1)
x=7
Next you have to find y, by putting 7 in for x.
y=4-2(7)
y=4-14
y=-10
The solution is (7,-10)
Elimination method
You are given two equations:
4x-y=16
3x-y=10
First you have to subtract 4x and 3x, and then you have to subtract -y and -y, and subtract 16 and 10. Then you have:
x=6
Now you have to find y, by substituting 6 for x in either original equation.
3(6)-y=10
18-y=10
y=18-10
y=8
The solution is (6,8)
Graphing method
On this method you can make a graph, and make the lines from the two given equations. For example you can use desmos.com. Then you just have to look at the exact coordinates of the point where the lines intersect from the graph.