How do you solve the system of equations #8x+4y=13# and #-2x=y+4#?

Question

Avery Alexander · Accepted Answer

See the entire solution process below:

First, sole the second equation for #y#: #-2x = y + 4# #-2x - color(red)(4) = y + 4 - color(red)(4)# #-2x - 4 = y + 0# #-2x - 4 = y# #y = -2x - 4# Step 2) Substitute #-2x - 4# for #y# in the first equation and solve for #x#: #8x + 4y = 13# becomes: #8x + 4(-2x - 4) = 13# #8x + (4 * -2x) - (4 * 4) = 13# #8x -8x - 16 = 13# #0 - 16 = 13# #-16 != 13# Therefore, there are no solutions to this problem. Or, the solution is the empty or null set: #{O/}#. This means the two lines defined by these equations are parallel and are not the same line.

Kennedy Adams · Answer

undefined To solve the system of equations:

1. Solve one equation for one variable.
2. Substitute the expression obtained in step 1 into the other equation.
3. Solve the resulting equation for the variable.
4. Substitute the value found in step 3 into one of the original equations to find the value of the other variable.
5. Verify the solution by checking that it satisfies both original equations.

Given the system:
1. 8x + 4y = 13
2. -2x = y + 4

From equation 2, solve for y:
   y = -2x - 4

Substitute y = -2x - 4 into equation 1:
   8x + 4(-2x - 4) = 13

Solve for x:
   8x - 8x - 16 = 13
   -16 = 13

This equation is inconsistent, indicating that the system has no solution.

Kennedy Adams · Answer

undefined To solve the system of equations $8x + 4y = 13$ and $-2x = y + 4$, you can use the substitution method or the elimination method. Let's use the substitution method:

1. Solve the second equation for one variable (let's solve for $y$):
$$ -2x = y + 4 \implies y = -2x - 4 $$

2. Substitute $y = -2x - 4$ into the first equation:
$$ 8x + 4(-2x - 4) = 13 $$

3. Simplify and solve for $x$:
$$ 8x - 8x - 16 = 13 \implies -16 = 13 $$
The equation is inconsistent, meaning there's no solution. Therefore, the system of equations has no solution.