Question

Solve the following pair of equations by the elimination method and the substitution method:

$3x+4y=10$ and $2x-2y=2$

• A. $x=1,y=6$
• B. $x=2,y=1$
• C. $x=1,y=2$
• D. $x=6,y=1$

Answer 1

The correct option is B $x=2,y=1$

Equations are:
$3x+4y=10...\left(1\right)$
$2x-2y=2...\left(2\right)$

Elimination Method
Multiplying eq$\left(1\right)$ by $1$ and eq$\left(2\right)$ by $2$ and adding will get
$\Rightarrow 1(3x+4y)+2(2x-2y)=1\times 10+2\times 2$
$\Rightarrow 3x+4y+4x-4y=10+4$
$7x=14$
$\Rightarrow x=2$
Now putting $x$ in eq$\left(1\right)$
$\Rightarrow 3\times 2+4y=10$
$\Rightarrow 6+4y=10$
$\Rightarrow 4y=4$
$\Rightarrow y=1$
Hence $x=2,y=1$

Substitution Method

From eq$\left(2\right)$ we get
$-2y=2-2x$
$\Rightarrow y=x-1$
Now substituting this $y$ in eq$\left(1\right)$
$\Rightarrow 3x+4(x-y)=10$
$\Rightarrow 3x+4x-4=10$
$\Rightarrow 7x=14$
$\Rightarrow x=2$
Now substituting $x$ in eq$\left(2\right)$
$\Rightarrow 2\times 2-2y=2$
$\Rightarrow 4-2y=2$
$\Rightarrow -2y=2-4$
$\Rightarrow -2y=-2$
$\Rightarrow y=1$
Hence $x=2,y=1$