When you solve a system of equations, what does the solution represent on the graph of the two equations
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We can solve this by substitution. Let's make the second equation equal y by adding y to both sides. The equation would look like:
x-5=y
Let's plug that equation in for y in the first equation.
2x+x-5-10=0
Let's add like terms.
2x+x-15=0
Let's add 15 to both sides.
2x+x=15
3x=15
Now divide.
15÷3=5=x
Now, x equals 5, so that means y equals 0. Let's check in both equations.
2(5)+0-10=0
10+0-10=0
0=0
5-0-5=0
0=0
So, the solution of the system shown is (5,0). I also included a graph so you could see where they intercept. The solution, when put in the graph, is the x intercept.
x-5=y
Let's plug that equation in for y in the first equation.
2x+x-5-10=0
Let's add like terms.
2x+x-15=0
Let's add 15 to both sides.
2x+x=15
3x=15
Now divide.
15÷3=5=x
Now, x equals 5, so that means y equals 0. Let's check in both equations.
2(5)+0-10=0
10+0-10=0
0=0
5-0-5=0
0=0
So, the solution of the system shown is (5,0). I also included a graph so you could see where they intercept. The solution, when put in the graph, is the x intercept.