i am lost with this one.
Solve the system by graphing. what is the soltion.
2x-2y=10
x+y=3
x=4
This is how the problem is with all thre equations. Help me please.....
put it in slope intercept form.
put both lines in slope intercept form.
2x-2y=10
x+y=3
y= x-5
y= -x + 3
now, plot the lines, where they cross is the solution.
To solve the system of equations by graphing, you first need to put both equations in slope-intercept form, which is of the form y = mx + b, where m represents the slope and b represents the y-intercept.
Let's start with the first equation, 2x - 2y = 10:
1. Move the y term to the other side of the equation: 2x - 10 = 2y.
2. Divide both sides of the equation by 2 to isolate the y term: (2x - 10)/2 = y.
3. Simplify the equation further: y = x - 5.
Now let's focus on the second equation, x + y = 3:
1. Move the x term to the other side of the equation: y = -x + 3.
With both equations now in slope-intercept form, we can graph them:
1. Determine the slope and y-intercept for each equation:
a. The equation y = x - 5 has a slope of 1 and a y-intercept of -5.
b. The equation y = -x + 3 has a slope of -1 and a y-intercept of 3.
2. Plot the y-intercept of each line on the graph. For the first line (y = x - 5), put a point on the y-axis at -5. For the second line (y = -x + 3), put a point on the y-axis at 3.
3. Use the slopes to find additional points on each line. The slope of 1 means that for every increase of 1 in the x-direction, the y-value increases by 1. The slope of -1 means that for every increase of 1 in the x-direction, the y-value decreases by 1. From the y-intercept, move 1 unit to the right and 1 unit up to find another point on the first line. For the second line, move 1 unit to the right and 1 unit down from the y-intercept.
4. Connect the dots for each line. Draw a line passing through the two points on each line.
5. The point where the lines intersect is the solution to the system of equations. In this case, the lines intersect at the point (4, -1).
Therefore, the solution to the system of equations is x = 4 and y = -1.