To solve linear equations in two variables by graphing, we have to understand how to draw the graph of linear equation.
Using slope and y-intercept, we can draw the graph.
Slope = rise / run
y-intercept is the point of the line where it crosses the y-axis.
What is solution ?
When we solve system of linear equations in two variables, the point of intersection is solution.
To find point of intersection of two lines, we have to graph the lines.
Solve each
system by graphing. Show your answer both graphically and as an ordered pair.
Problem 1 :
y = x + 1
y = (-2/3)x – 4
Solution :
y = x + 1 ----(1)
y = (-2/3)x – 4 ----(2)
From (1), slope = 1 and y-intercept = 1
Slope = Rise / Run ==> 1/1
From y-intercept move 1 unit right and 1 unit up. Like this mark two more points and draw the line.
From (2), slope = -2/3 and y-intercept = -4
Slope = Rise / Run ==> -2/3
From y-intercept move 2 units left and 3 units up. Like this mark two more points and draw the line.
The point of intersection of these two lines is (-3, -2). So, the solution is (-3, -2).
Problem 2 :
y = -x – 4
y = x + 2
Solution :
y = -x – 4 -----(1)
y = x + 2 -----(2)
From (1), slope = -1 and y-intercept = -4
Slope = Rise / Run ==> -1/1
From y-intercept move 1 unit left and 1 unit up. Like this mark two more points and draw the line.
From (2), slope = 1/1 and y-intercept = 2
Slope = Rise / Run ==> 1/1
From y-intercept move 1 unit left and 1 unit up. Like this mark two more points and draw the line.
The point of intersection of these two lines is (-3, -1). So, the solution is (-3, -1).
Problem 3 :
x – y = 4
3x + y = 4
Solution :
x - y = 4
y = x - 4-----(1)
3x + y = 4
y = -3x + 4-----(2)
From (1), slope = 1 and y-intercept = -4
Slope = Rise / Run ==> 1/1
From y-intercept move 1 unit right and 1 unit up. Like this mark two more points and draw the line.
From (2), slope = -3/1 and y-intercept = 4
Slope = Rise / Run ==> -3/1
From y-intercept move 3 units left and 1 unit up. Like this mark two more points and draw the line.
The point of intersection is (2, -2). So, the solution is (2, -2).
Problem 4 :
3x – 2y = 4
3x + 2y = 8
Solution :
3x - 2y = 4
2y = 3x - 4
y = (3/2) x - 2-----(1)
3x + 2y = 8
2y = -3x + 8
y = (-3/2)x + 4-----(2)
From (1), slope = 3/2 and y-intercept = -2
Slope = Rise / Run ==> 3/2
From y-intercept move 3 units left and 2 units up. Like this mark two more points and draw the line.
From (2), slope = -3/2 and y-intercept = 4
Slope = Rise / Run ==> -3/2
From y-intercept move 3 units left and 2 units up. Like this mark two more points and draw the line.
The point of intersection of these two lines is (2, 1). So, the solution (2, 1).
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM