Verified Answer :

lime52

7x - 3y = 13
x - 2y = 5

To solve a system of equations, we first need to solve for one of the variables. In this case, let's solve for x.

7x - 3y = 13   Given
7x = 3y + 13   Add 3y to both sides
x = 3/7y + 13/7   Divide both sides by 7

x - 2y = 5   Given
x = 2y + 5   Add 2y to both sides

Now we can set the two equations equal to each other, since they both equal x.

3/7y + 13/7 = 2y + 5   Set the equations equal to each other
13/7 = 11/7y + 5   Subtract 3/7y from both sides; 2 can also be written as 14/7, since 14 divided by 7 is 2, so just subtract 3 from 14
-22/7 = 11/7y   Subtract 5 from both sides
-2 = y   Multiply both sides by 7/11, since you multiply fractions by their reciprocal to cancel; you might want to use a calculator for this

Now we know that y = -2. Let's substitute that into one of our original equations to get x.

x = 2y + 5   Given
x = 2(-2) + 5   Substitute y for -2
x = -4 + 5   Multiply
x = 1   Add

The answer is x = 1, y = -2.

Hope this helps!

Solutions 

To solve the equation we have to use substitution. "Substitution" means putting numbers where the letters are placed. 

Calculations 

1) Solve for x in x−2y=5 

 ⇒ Solve for x

x−2y=5

⇒ Add 2y to each side

x=5+2y

2)  Substitute x=5+2y into 7x−3y=13 

⇒ Start with the original equation 

7x−3y=13

⇒ Let x=5+2y

7(5+2y)−3y=13

⇒ Simplify

35+11y=13

3) Solve for y in 35+11y=13 

⇒ Solve for y

35+11y=13

⇒Subtract 35 from both sides

11y=13−35

⇒ Simplify 13−35 to −22

11y=−22

⇒ Divide both sides by 11

y=−22 ÷ 11

⇒ Simplify 22 ÷ 11 to 2y=−2
y= -2

4) Substitute y=−2 into x=5+2y 

⇒ Start with the original equation
 
x=5+2y

⇒ Let y=−2

x=5+2×−2

⇒ Simplify

x=1 

Therefore,

x=1

y=−2