Solve each pair of equations by substituting

2x + y = 3

4x + 3y = 1

the value of x and y is 4 and - 5 respectively.

Step-by-step explanation:

from the equation we say let;

2x + y = 3 ... equation 1

4x + 3y = 1 ... equation 2

from equation 1

2x + y = 3 ... equation 1

y = 3 - 2x ... equation 3

Substitute for y in equation 2

4x + 3y = 1 ... equation 2

we have,

4x + 3 (3 - 2x) = 1

4x + 9 - 6x = 1

we have to collect the like terms

9-1 = 6x - 4x

8 = 2x

divide both sides by 2

8/2 = 2x/2

4 = x

therefore x = 4

put x = 4 in equation 3

y = 3 - 2x ... equation 3

y = 3 - 2 (4)

y = 3 - 8

y = - 5

therefore the value of x and y is 4 and - 5 respectively.

to check if your answer is correct, put the value of x and y in any of the equations.

2x + y = 3 ... equation 1

2 (4) + (-5) = 3

8 - 5 = 3

3 = 3 ... proved

Step: Solve

2

x

+

y

=

3

for y:

2

x

+

y

=

3

2

x

+

y

+

-

2

x

=

3

+

-

2

x

(Add - 2x to both sides)

y

=

-

2

x

+

3

Step: Substitute

-

2

x

+

3

for

y

in

4

x

+

3

y

=

1

:

4

x

+

3

y

=

1

4

x

+

3

(

-

2

x

+

3

)

=

1

-

2

x

+

9

=

1

(Simplify both sides of the equation)

-

2

x

+

9

+

-

9

=

1

+

-

9

(Add - 9 to both sides)

-

2

x

=

-

8

-

2

x

-

2

=

-

8

-

2

(Divide both sides by - 2)

x

=

4

Step: Substitute

4

for

x

in

y

=

-

2

x

+

3

:

y

=

-

2

x

+

3

y

=

(

-

2

)

(

4

)

+

3

y

=

-

5

(Simplify both sides of the equation)

Answer:

x

=

4

and

y

=

-

5