proportion and percent

Question

Solve the system by graphing both lines on one coordinate system.

23) x - y = -4

2x + y = -2

Solve the system of equations by the method of elimination.

24) 4x + 6 y = 8

12x - 4 y = -20

Answer 1

23)

 

To solve graphically, you will need to draw the two lines that the equations represent on the same coordinate system.  Then, you find the point where the two lines intersect.

 

 

You will need to put both equations in y=mx+b form.

 

x - y = -4     ----->    -y = -x - 4   ------>   y = x + 4

 

x + y = -2    ----->     y = -x - 2

 

 

You will graph the two bold equations on the coordinate system.  Find the point where the lines intersect.  That point of intersection is the solution (x, y).

 

 

24)

 

To solve by elimination means to manipulate the equation by either multiplying or subtracting or adding the equations in order to eliminated an x or y term, giving only one equation with one variable.

 

Multiplying the first equation by 3 and keeping the second equation gives

 

12x + 18y = 24

12x - 4y = -20

 

 

Subtracting the second equation from the first equation gives

 

22y = 44

 

 

Now we have a single equation with one variable.  Solve for y from this equation.

 

y = 2

 

 

Substitute this value of y into the first equation to solve for x.

Answer 2

Hi Cory,

 

 

Solve the system by graphing both lines on one coordinate system.

23) x - y = -4

2x + y = -2

Solve the system of equations by the method of elimination.

24) 4x + 6 y = 8

12x - 4 y = -20

 

 

23) x - y = -4                 2x + y = -2
      x+4=y                             y=-2x-2  

      y=x+4  The slope is 1 and the y-intercept is 4.

     y=-2x-2 the slope is -2 and the y-intercept is -2

 

   After graphing both lines identify the point where the lines intercept.  That is the graphical solution to the system of equations. 

 

x+4=-2x-2           y=x+4

3x+4=-2              y=-2+4

3x=-6                  y=2

x=-2                              The point where the two lines intercept is (-2,2)

 

Solve the system of equations by the method of elimination.

24)

4x + 6 y = 8           -3[4x + 6 y = 8 ]        -12x-18y=-24
12x - 4 y = -20         12x - 4 y = -20         12x - 4 y = -20

                                                               ----------------

                                                                     -22y=-44

                                                                          y=2

 

Substitute y=2 into first equation

4x + 6 y = 8

4x+6(2)=8

4x+12=8

4x=-4

x=-1

 

The solution is (-1,2)

 

that's it...