How do solve the following linear system?: # y=-3x+4 , -6x-2y=-8 #?

Question

How do solve the following linear system?: #  y=-3x+4  ,    -6x-2y=-8   #?

Eva Abramson · Accepted Answer

There is an infinite number of solutions.

#y=−3x+4# #−6x−2y=−8# Rewrite the equations in standard form of #Ax+By=C#: #3x+y=4# #6x+2y=8# Notice that the 2nd equation is just the 1st one multiplied by 2, which means that the lines coincide. Therefore, the equations have the same graph and every solution of one equation is a solution of the other. There is an infinite number of solutions. This is a "Consistent, Dependent System".

Jameson Allen · Answer

undefined To solve the linear system:

1. Substitute the expression for y from the first equation into the second equation:
   -6x - 2(-3x + 4) = -8

2. Distribute the -2:
   -6x + 6x - 8 = -8

3. Simplify and solve for x:
   0x - 8 = -8
   -8 = -8

4. Since -8 = -8 is always true, the system has infinitely many solutions and is dependent.

5. To find the y-coordinate, use either of the original equations. Let's use the first equation:
   y = -3x + 4

6. Substitute the value of x from step 3 into the equation:
   y = -3(0) + 4
   y = 4

Therefore, the solution to the system is (0, 4).