Question

solving a system of linear equations using substitution
solve this system of equations using substitution
$y = 2x - 4$
$x + 2y = 10$
step 5: which step isolates the variable term on the left side?
add 8
divide by 5
step 6: to solve for $y$, substitute 3.6 for $x$ in the ____ equation
step 7: which is the $y$-value in the solution?
$y = $
options: -0.8, 1.6, 3.2
on the right side (calculation steps):
$x + 2(2x - 4) = 10$
$x + 4x - 8 = 10$
$5x - 8 = 10$
$\\ \\ \\ \\ \\ \\ \\ + 8 \\ \\ \\ + 8$
$5x = 18$
$x = 3.6$
$y = 2x - 4$
$y = 2(3.6) - 4$

Explanation:

Step1: Substitute $y=2x-4$ into second equation

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

Step2: Expand and simplify the equation

$x + 4x - 8 = 10 \implies 5x - 8 = 10$

Step3: Isolate the $x$-term

$5x = 10 + 8 \implies 5x = 18$

Step4: Solve for $x$

$x = \frac{18}{5} = 3.6$

Step5: Substitute $x=3.6$ into $y=2x-4$

$y = 2(3.6) - 4$

Step6: Calculate the value of $y$

$y = 7.2 - 4 = 3.2$

Answer:

$y = 3.2$