Question

Difficulty: EasySystems of Linear Equations

If $x + y = 8$ and $2x - y = 7$ , what is the value of $x$ ?

Adding the two equations yields

(x + y) + (2x - y) = 8 + 7

, which simplifies to

3x = 15

. Dividing both sides by 3 gives the correct value,

x = 5

Add the two equations together to eliminate the variable

y

(x + y) + (2x - y) = 8 + 7 \implies 3x = 15

Since the coefficients of

y

are

+1

and

-1

, adding the equations eliminates

y

directly.

Solve for

x

by dividing both sides of the equation by 3.

x = \frac{15}{3} = 5

Isolating

x

gives the required solution.

Elimination Method in Systems of Linear Equations

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