Question

solve by substitution method
a) 2x+3y=7 b) 2x+y=28

Answer 1

Answer :-

• X = $\sf \frac{77}{4} \: \: and\: \: Y = - \frac{21}{2}$

Explanation :-

Substitute method :-

• 2x + 3y = 7 _______(1)
• 2x + y = 28 _______(2)

• Now make substitute equation in eq. (2)
• 2x + y = 28 _______(2)
• 2x = 28 - y
• $\sf x = \frac{28 - y}{2}$ ______(3)

Now, put the value of eq.(3) in eq. (1) then,

• 2x + 3y = 7 _______(1)

• $\sf 2 \bigg( \frac{28 - y }{2} \bigg) + 3y = 7$

• $\sf \cancel{2} \bigg( \frac{28 - y }{\cancel{2}} \bigg) + 3y = 7$

• $\sf 28 - y + 3y = 7$

• $\sf 28 + 2y = 7$

• $\sf 2y = 7 - 28$

• $\sf 2y = - 21$

• $\sf \red{ y = - \frac {21}{2} }$

Now, put the value of y in eq.(3)

• $\sf x = \frac{28 - y}{2}$

• $\sf x = \frac{28 - \bigg(-\frac{21}{2}\bigg)}{2}$

• $\sf x = \frac{28 + \bigg( \frac{21}{2}\bigg)}{2}$

• $\sf x = \frac{ \frac{56+21}{2}}{2}$

• $\sf x = \frac{ \frac{77}{2}}{2}$

• $\sf x = \red{ \frac {77}{4} }$

Hence, $(x,y) = \bigg(\frac{77}{4} , -\frac{21}{2} \bigg)$

I hope it helps you ❤️✔️