Plotting Points Method
For y = x+1, let the first 7 coordinates be:
x = 0, 1, 2, 3, 4, 5, 6
y = 1, 2, 3, 4, 5, 6, 7
For y = -x+7, let the first 7 coordinates be:
x = 0, 1, 2, 3, 4, 5, 6
y = 7, 6, 5, 4, 3, 2, 1
Plot the graph and where the lines intersect that will be the solution to the simultaneous equation:
x = 3 and y = 4 -- (3,4).
Slope Intercept Method
For y = x + 1, the y-intercept is 1 (the point (0,1)) and the slope is 1.
You can graph y = x + 1 by plotting the point (0,1) and drawing a line with slope of 1 (through the point (1, 2) for example).
For y = -x + 7, the y-intercept is 7 (the point (0,7)) and the slope is -1.
To graph the function, plot the point (0,7) and draw the line with slope -1 through that point (through the point (1,6) would work).
The solution to the system is found by substituting x + 1 for y in the second equation:
y = x + 1
y = -x + 7
x + 1 = -x + 7
2x = 6
x = 3.
y = x + 1
y = 3 + 1 = 4.
So the solution is at the point (3,4).
the solution to a system is where the two lines intersect upon a graph.
The graph shifts downward (negative y) by 9 units.
One solution
Graph both and where they cross is the answer to both.
You plot the equation as a graph. Every one of the infinitely many points on the graph is a solution.
A graph that has 1 parabolla that has a minimum and 1 positive line.
the solution to a system is where the two lines intersect upon a graph.
Graph both equations on the same graph. Where they intersect is the solution to the system of equations
The graph shifts downward (negative y) by 9 units.
one solution
One solution
Graph both and where they cross is the answer to both.
The statement - The graph of a system of equations with the same slope and the same y intercepts will have no solution is True
You plot the equation as a graph. Every one of the infinitely many points on the graph is a solution.
negative one and a half
If the discriminant is negative, the equation has no real solution - in the graph, the parabola won't cross the x-axis.
No Solutions