What are x and y if #10x - 2y = -8# and #3y - 5x = 8#?

Question

What are x and y if  #10x - 2y = -8# and #3y - 5x = 8#?

Eva Adamson · Accepted Answer

#(x,y) = (-2/5,2)# Given [1]#color(white)("XXX")10x-2y = -8# [2]#color(white)("XXX")3y-5x=8# Rearrange [2] into standard form order: [3]#color(white)("XXX")-5x+3y=8# Multiply [3] by #2# to make coefficients of #x# in [1] and [4] additive inverses [4]#color(white)("XXX")-10x+6y = 16# Add [1] and [4] [5]#color(white)("XXX")4y=8# Divide [5] by #2# [6]#color(white)("XXX")y=2# Substitute #2# fro #y# in [1] [7]#color(white)("XXX")10x-2(2)=-8# [8]#color(white)("XXX")10x -4 = -8# [9]#color(white)("XXX")10x = -4# [10]#color(white)("XXX")x=-2/5#

Jameson Allen · Answer

undefined To solve the system of equations $10x - 2y = -8$ and $3y - 5x = 8$, you can use the substitution method. Here's how you do it:

1. Rearrange the first equation to solve for $x$:
   $10x - 2y = -8$ becomes $10x = 2y - 8$, which simplifies to $x = \frac{2y - 8}{10}$ or $x = \frac{y - 4}{5}$.

2. Substitute the expression for $x$ from the first equation into the second equation:
   $3y - 5\left(\frac{y - 4}{5}\right) = 8$.

3. Simplify the equation and solve for $y$:
   $3y - y + 4 = 8$,
   $2y + 4 = 8$,
   $2y = 4$,
   $y = 2$.

4. Substitute $y = 2$ back into the expression for $x$ to find $x$:
   $x = \frac{2(2) - 8}{10}$,
   $x = \frac{4 - 8}{10}$,
   $x = \frac{-4}{10}$,
   $x = -0.4$.

So, the solution to the system of equations is $x = -0.4$ and $y = 2$.