Question

Alex is solving this system of equations: 5x + 4y = 1 4x + 2y = 8 He starts by rearranging the second equation to isolate the y variable: y = 4 - 2x. He then substitutes the expression 4 - 2.c for y in the first equation, as shown: Step 1: 5x +4(4-22) 1 Step2: 50 + 16 - 8x = 1 -32 = -15 Step 3: Step 4: I= -5 Step 5: y=4 - 2x Step 6: y=4-2(-5) Step 7: y= 14 Where did Alex make a mistake? Step 6

Answer 1

Answer:

Step 4

Explanation:

The initial system of equation is:

5x + 4y = 1

4x + 2y = 8

So, if we take the second equation and isolate y, we get:

y = 4 - 2x

Then, replacing it on the first one, we get:

5x + 4(4 - 2x) = 1

Solving for x, we get:

5x + 4*4 - 4*2x = 1

5x + 16 - 8x = 1

-3x +16 = 1

-3x + 16 - 16 = 1 - 16

-3x = -15

Finally, dividing by -3, we get:

$\begin{gathered} \frac{-3x}{-3}=\frac{-15}{-3} \\ x=5 \end{gathered}$

Therefore, the mistake was made in step 4, because he didn't take into account the negative sign. So, the correct answer is x = 5 instead of x = - 5