how do you solve each linear system by graphing y=x+3, y=-2x+6

Question

solve each linear system by graphing. check your answer

Answer 1

Given equations are y = x+3

y = -2x+6

To find coordinate pairs substitute x = 0,1,-1 in above equations.

Then the coordinate points of first equation would be (0,3),(1,4),(-1,2).

Points of second equation would be (0,6),(1,4),(-1,8).

Graph of above equation.

Draw the coordinate plane.

Plot the above points.

Connect the plotted points.

Then the formed lines indicating given equations.

Observe the graph the two lines are intersecting at (1,4)

Solution of given system is x = 1, y = 4.

Check:

Substitute x, y values in given equations.

y = x+3

4 = 1+3

4 = 4

y = -2x+6

4 = -2*1+6

4 = 4

Solution is satisify the given linear system.

Answer 2

The system of linear equations are y = x + 3 and y = - 2x + 6.

Write the equations in slope - intercept form : y = mx + b, where m is slope and b is y - intercept.

The first linear equation is y = x + 3.

It is already in slope - intercept form.

So, compare the equation with slope - intercept form : y = mx + b.

slope = - 1 and y - intercept is 3.

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

Using slope find the next point.

Slope = rise/run = 1/1

Start at point (0, 3), move 1 unit up and 1 unit right, then plot the point (1, 4).

The second linear equation is y = - 2x + 6.

It is also in slope - intercept form.

So, compare the equation with slope - intercept form : y = mx + b.

slope = - 2 and y - intercept is 6.

y - intercept is 6, so the line crosses the y - axis at (0, 6)

Using slope find the next point.

Slope = rise/run = - 2/1

Start at point (0, 6), move 2 units down and 1 unit right, then plot the point (1, 4).

Draw the lines through these points.

Graph :

Observe the graph, the solution of the linear system (x, y ) = (1, 4).

Check :

Substitute the values x = 1 and y = 4 in given linear system.

y = x + 3           and        y = - 2x + 6

4 = 1 + 3                         4 = - 2(1) + 6

4 = 4.                              4 = - 2 + 6

                                       4 = 4.

The above statements are true.

So, the solution of the given linear system (x, y ) = (1, 4).