Question

Solve the following simultaneous equations:

$3x+2y=14$, $-x+4y=7$

• A. $x=0;y=-4$
• B. $x=3;y=2.5$
• C. $x=3.5;y=-2$
• D. $x=4.5;y=3$

Answer 1

The correct option is B $x=3;y=2.5$

We pick either of the equations and write one variable in terms of the other.

Let us consider the equation $-x+4y=7$ and write it as

$x=4y-\mathrm{7...........}\left(1\right)$

Substitute the value of $x$ in Equation $3x+2y=14$. We get

$3(4y-7)+2y=14$

i.e. $12y-21+2y=14$

i.e. $14y=35$

i.e. $2y=5$

Therefore, $y=\frac{5}{2}=2.5$

Substituting this value of $y$ in Equation (1), we get

$x=10-7=3$

Hence, the solution is $x=3,y=2.5$.