Can you please solve the system of equations by graphing x-y-4=0 and x+y-2=0 and show work so I can understand
cannot show graphs here.
But if you draw the graphs for the two lines, you will see that they intersect at (3,-1)
If you do not know how to graph a line, there are many examples online and, no doubt, in your lesson material.
It was right but Can you show how you got that answer please so I can do the others
First equation
x - y - 4 = 0
Add y to both sides
x - 4 = y
y = x - 4
Second equation
x + y - 2 = 0
Subtract x to both sides
y - 2 = - x
Add 2 to both sides
y = - x + 2
Draw Cartesian coordinate system.
Find x-intercept and y-intercept for both equations.
The x-intercept is the point at which the graph crosses the x-axis.
At this point, the y-coordinate is zero.
The y-intercept is the point at which the graph crosses the y-axis.
At this point, the x-coordinate is zero.
First equation
y = x - 4
x-intercept
0 = x - 4
Add 4 to both sides
4 = x
x = 4
Mark point ( 4 , 0 )
y-intercept
y = x - 4
y = 0 - 4
y = - 4
Mark point ( 0 , - 4 )
Connect these two points with a straight line.
Second equation
y = - x + 2
x-intercept
0 = - x + 2
Add x to both sides
x = 2
Mark point ( 2 , 0 )
y-intercept
y = - x + 2
y = 0 + 2
y = 2
Mark point ( 0 , 2 )
Connect these two points with a straight line.
The point where two lines meet is the solution of your system of equations.
x = 3 , y = - 1
Of course! To solve the system of equations by graphing, we need to graph both equations on the same coordinate plane and find the point where the two graphs intersect. This point represents the solution to the system.
Let's start with the first equation: x - y - 4 = 0.
To graph this equation, we need to rearrange it into the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Rearranging the equation, we get: y = x - 4.
Now, we can find two points on the graph by plugging in values for x and solving for y. For simplicity, let's choose x = 0 and x = 5.
For x = 0:
y = 0 - 4 = -4, so we have the point (0, -4).
For x = 5:
y = 5 - 4 = 1, so we have the point (5, 1).
Now, let's plot these two points on the coordinate plane and draw a line passing through them.
Moving on to the second equation: x + y - 2 = 0.
Similarly, rearrange this equation into slope-intercept form:
y = -x + 2.
Again, let's find two points on the graph by plugging in values for x. Let's choose x = 0 and x = 3.
For x = 0:
y = -0 + 2 = 2, so we have the point (0, 2).
For x = 3:
y = -3 + 2 = -1, so we have the point (3, -1).
Plot these two points on the same graph.
Now, observe the graph. The point of intersection is the solution to the system of equations. In this case, it appears that the lines intersect at the point (1, -3).
Therefore, the solution to the system of equations x - y - 4 = 0 and x + y - 2 = 0 is x = 1 and y = -3.
Graphing the equations visually and looking for the point of intersection is a helpful way to solve simple systems of equations. However, for more complex systems, it may be more efficient to use algebraic methods like substitution or elimination.