Linear Equations

Question

Solve the systems of linear equations by using the method of substitution. If the system is consistent, inconsistent, or dependent, say so in your answer. 3x+4y=8    y=-3/4x+4

Answer 1

3x + 4y = 8              y = 3/4x + 4                          GRAPH ANSWERS FROM LEFT

substitute 0 for x in both equations                 x = 0   y = 2       x = 0   y = 4

ANSWER                                                             x = 4    y = -1     x = 4   y = 1

x = 0 y = 2               x = 0 y = 4                             OR

SOLUTION               SOLUTION                            (0,2) (0,4) and (4,-1) (4,1)

3(0) + 4y = 8           y = 3/4 (0) + 4                      If you keep plotting points, you will see that the lines

0 + 4y = 8               y = 0 + 4                              are parallel.  The first line is 2 below the second line.

4y = 8                     y = 4                                    So the Linear Equations are Inconsistent (parallel lines)

divide by 4

y = 2

substitute 4 for x in both equations

ANSWER

x = 4  y = -1             x = 4  y = 1

SOLUTION               SOLUTION

3(4) + 4y = 8           y = -3/4(4) + 4

12 + 4y = 8             y = -3 + 4

Subtract 12              y = 1

4y = -4

Divide by 4

y = -1

 

 

Answer 2

Assuming you mean eq1. 3x+4y=8 and eq2. y=(-3/4)x+4, then using substitution you can simply input eq2 into eq1

first sub eq2 for y in eq 1:   3x+4[(-3/4)x+4]=8 

next distribute 4:                3x+(-3x+16)=8

drop parenthesis:               3x-3x+16=8

combine like terms:            0x+16=8

so your result is:                  16=8, which has no solution and is therefore inconsistent