Question

solve the following system of equation by substitution method 5x-7y=11 and 7x+4y=5​

Answer 1

Answer:

The above picture is the answer

Answer 2

The values of x and y are $\frac{79}{69}$ and $-\frac{52}{69}$ respectively

Step-by-step explanation:

Given equations are $5x-7y=11\hfill (1)$ and

$7x+4y=5\hfill (2)$

To solve the given system of equations by Substitution method :

• From equation (1) $5x-7y=11$
• $5x=11+7y$

Therefore $x=\frac{11+7y}{5}$

Now substitute the value of x in the equation (2) we get

• $7(\frac{11+7y}{5})+4y=5$
• $\frac{77+49y}{5}+4y=5$
• $\frac{77+49y+20y}{5}=5$
• $\frac{77+69y}{5}=5$
• $77+69y=5\times 5$
• $69y=25-77$

Therefore $y=-\frac{52}{69}$

Now substitute the value of y in the equation $x=\frac{11+7y}{5}$ we get

• $x=\frac{11+7(-\frac{52}{69})}{5}$
• $=\frac{11-\frac{364}{69}}{5}$
• $=\frac{69(11)-364}{69\times 5}$
• $=\frac{759-364}{345}$
• $=\frac{395}{345}$
• $=\frac{79}{69}$

Therefore $x=\frac{79}{69}$

Therefore the values of x and y are $x=\frac{79}{69}$ and $y=-\frac{52}{69}$