How would i graph and solve these pair of simultaneous equations.

Question

1) y = 1/2x y= x+1 2) y=-x+4 y=2x+1? 

 

Please Help... 
P.S the forward slash is a fraction

 

Answer 1

Graphing method

1) The equations are y = x/2  and y = x + 1

First line y = x/2

Compare the equation with slope-intercept form y = mx + b.

slope = 1/2 and y -intercept is 0.

y -intercept is 0, so the line crosses the y -axis at (0, 0)

Using slope find the next point.

Slope = rise/run = 1/2

Start at point (0, 0), move 1 unit up and 2 units right, then plot the point (2, 1).

Draw a line through these points.

Now  the second line y =  x + 1

slope = 1 and y -intercept is 1.

y -intercept is 1, so the line crosses the y -axis at (0, 1)

Using slope find the next point.

Slope = rise/run = 1/1

Start at point (0, 1), move 1 unit up and 1 unit right, then plot the point (1,2).

Draw a line through these points.

From the graph the lines are intersecting at (-2, -1).

Solution of the equations is x = - 2 and  y = - 1.

 

Answer 2

Graphing method

1) The equations are y = - x + 4  and y = 2x + 1

First line y = - x + 4

Compare the equation with slope-intercept form y = mx + b.

slope = - 1 and y -intercept is 4.

y -intercept is 4, so the line crosses the y -axis at (0, 4)

Using slope find the next point.

Slope = rise/run = -1

Start at point (0, 4), move 1 unit down and 1 unit right, then plot the point (2, 1).

Draw a line through these points.

Now  the second line y =  2x + 1

slope = 2 and y -intercept is 1.

y -intercept is 1, so the line crosses the y -axis at (0, 3)

Using slope find the next point.

Slope = rise/run = 2/1

Start at point (0, 1), move 2 unit up and 1 unit right, then plot the point (1,3).

Draw a line through these points.

From the graph the lines are intersecting at (1, 3).

Solution of the equations is x = 1 and  y = 3.