How do you solve by substitution #3x + 2y = 11# and #x - 2 = -4y#?

Question

Kennedy Adams · Accepted Answer

#(4,-1/2)# #3x+2y=11 and x-2 =-4y# Step 1:Choose an equation #x-2 =-4y# Step 2: Isolate a variable #x =-4y +2# Step 3: Substitute #-4y +2# for #x# in the other equation #3(-4y+2)+2y=11 # Step 4:Distribute #-12y+6+2y=11 # Step 5:Simplify #-10y=5# Step 6: Find #y# value #y=-1/2# Step 7: Plug y value back into any equation #x-2 =-4(-1/2)# Step 8:Solve for "x " #x=4#

Jameson Allen · Answer

undefined To solve the system of equations by substitution, we first solve one of the equations for one variable and then substitute that expression into the other equation.

In this case, let's solve the second equation, $ x - 2 = -4y $, for $ x $:
$$ x = -4y + 2 $$

Now, substitute this expression for $ x $ into the first equation:
$$ 3(-4y + 2) + 2y = 11 $$

Now, solve for $ y $:
$$ -12y + 6 + 2y = 11 $$
$$ -10y + 6 = 11 $$
$$ -10y = 5 $$
$$ y = -\frac{1}{2} $$

Now that we have found the value of $ y $, substitute it back into one of the original equations to find the value of $ x $. Using the second equation:
$$ x - 2 = -4(-\frac{1}{2}) $$
$$ x - 2 = 2 $$
$$ x = 4 $$

Therefore, the solution to the system of equations is $ x = 4 $ and $ y = -\frac{1}{2} $.