Graph the two equations to solve the system. Write the ordered pair solution like this (1,2) with no spaces, or write no solution or infinitely many solutions.
x + y = 6 and x - y = 4
Find ordered pairs to graph these equations.
x + y = 6
x = 0, y = 6
x = 2, y = 4
x = 4, y = 2
x = 6, y = 0
x - y = 4
Do the same for this equation.
Plot the points, for each equation and draw a line for each set of points.
The point of intersection is the solution.
To graph the two equations and solve the system, we can use the method of substitution.
First, let's solve one of the equations for one variable in terms of the other.
Let's solve the first equation, x + y = 6, for x:
x = 6 - y
Now we can substitute this expression for x into the second equation, x - y = 4:
(6 - y) - y = 4
Simplifying this equation:
6 - 2y = 4
-2y = 4 - 6
-2y = -2
y = -2 / -2
y = 1
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation, x + y = 6:
x + 1 = 6
x = 6 - 1
x = 5
Therefore, the solution to the system of equations is the ordered pair (x, y) = (5, 1).
To graph these equations, we can create a coordinate system and plot the points that satisfy each equation.
For the equation x + y = 6, we can assign different values to x and solve for y.
When x = 0, y = 6.
When x = 1, y = 5.
When x = 3, y = 3.
Plotting these points and drawing a straight line through them will give us the graph of the equation x + y = 6.
For the equation x - y = 4, we can do the same process.
When x = 0, y = -4.
When x = 1, y = -3.
When x = 3, y = -1.
Plotting these points and drawing a straight line through them will give us the graph of the equation x - y = 4.
The point where these two lines intersect represents the solution to the system of equations.
Therefore, the graph of the system of equations would show two lines intersecting at the point (5, 1).