Question

in the solution of the system of equations, what is the value of x?
x + 2y = 6
3x - y = -10
4
-2
-4
2
question 6
the solution set of |2x - 3| = 7 is:
{-5, 2}
{5}
{5, -2}
{-2}

Explanation:

Step1: Isolate $y$ from second equation

From $3x - y = -10$, rearrange to get $y = 3x + 10$.

Step2: Substitute $y$ into first equation

Substitute $y = 3x + 10$ into $x + 2y = 6$:
$x + 2(3x + 10) = 6$
Expand: $x + 6x + 20 = 6$
Combine like terms: $7x + 20 = 6$

Step3: Solve for $x$

Subtract 20 from both sides: $7x = 6 - 20 = -14$
Divide by 7: $x = \frac{-14}{7} = -2$

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Step1: Split absolute value equation

For $|2x - 3| = 7$, split into two cases:
Case 1: $2x - 3 = 7$
Case 2: $2x - 3 = -7$

Step2: Solve Case 1

$2x = 7 + 3 = 10$
$x = \frac{10}{2} = 5$

Step3: Solve Case 2

$2x = -7 + 3 = -4$
$x = \frac{-4}{2} = -2$

Answer:

For the system of equations: $\boldsymbol{-2}$ (corresponding to option -2)
For the absolute value equation: $\boldsymbol{\{-2, 5\}}$ (corresponding to option $\{-2,5\}$)