Question

solving a system of linear equations using substitution
solve this system of equations using substitution:
\\( y = 2x - 4 \\)
\\( x + 2y = 10 \\)
step 3: which terms can be combined to isolate the variable term the left side? ( x ) and ( 4x )
step 4: which step isolates the variable term on the left side?
add 8
step 5: which step isolates the variable term on the left side?
options: add 5, subtract 5, divide by 5

Explanation:

Step1: Substitute y into second equation

$x + 2(2x - 4) = 10$

Step2: Distribute the 2

$x + 4x - 8 = 10$

Step3: Combine like terms

$5x - 8 = 10$

Step4: Isolate variable term (add 8)

$5x = 18$

Step5: Isolate x (divide by 5)

$x = \frac{18}{5}$

Step6: Solve for y (substitute x)

$y = 2(\frac{18}{5}) - 4 = \frac{36}{5} - \frac{20}{5} = \frac{16}{5}$

Answer:

Step 5: Divide by 5
Final solution: $x=\frac{18}{5}$, $y=\frac{16}{5}$