Question

Solve each of the following systems of equations by substitution

Answer 1

1) The solution to the given equations is (3,6)

2) The solution to the given equations is (7,-1)

3) The solution to the given equations is (6,5)

Explanation:

1) Given equations are
`x+y=5\hfill (1)`

and
`x=1+y\hfill (2)`

To solve the given equations by substitution method :

From equation (2) we have the value x=1+y

Substitute the value of x=1+y in equation (1) we get

(1+y)+y=5

1+y+y=5

1+2y=5

2y=5-1

2y=4

`y=(4)/(2)`

Therefore y=2

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

x=1+y

x=1+2

Therefore x=3

The solution is (3,6)

2) Given equations are
`2x+3y=11\hfill (1)`

and
`x+y=6\hfill (2)`

To solve the given equations by substitution method :

From equation (2) we have the value x=6-y

Substitute the value of x=6-y in equation (1) we get

2(6-y)+3y=11

12-2y+3y=11

y=11-12

Therefore y=-1

Now substitute the value of y=-1 in equation (2) we get

x+(-1)=6

x=6+1

Therefore x=7

The solution is (7,-1)

3) Given equations are
`x-y=1\hfill (1)`

and
`6x-7y=1\hfill (2)`

To solve the given equations by substitution method :

From equation (1) we have the value x=1+y

Substitute the value of x=1+y in equation (2) we get

6(1+y)-7y=1

6+6y-7y=1

-y=1-6

Therefore y=5

Now substitute the value of y=5 in equation (1) we get

x-5=1

x=1+5

Therefore x=6

The solution is (6,5)