Question

Which ordered pair is a solution to the system of equations? Use any method to solve. 4x-y=5, x+y=10

Answer 1

(3,7)

Explanation:

Given equations are

4x-y= 5 eq(1)

x+y= 10 eq(2)

we have to solve the system of equations by find an ordered pair.

we use substitution method to find solution of system of equations.

From eq(2)

y= 10-x

Putting above equation in eq(2),we get

4x-(10-x)=5

4x-10+x=5

4x+x-10=5

Add like terms

5x-10=5

Adding 10 to both sides of above equation,we get

5x-10+10= 5+10

5x=15

Dividing by 5 to both sides of above equation,we get

5x/5= 15/5

x= 3

Putting the value of x in eq(2) ,we get

3+y=10

Adding -3 to both sides of above equation,we get

-3+3+y=-3+10

0+y= 7

y= 7

Hence, (3,7) is solution of given system of equation.

Answer 2

The ordered pair ( 5, 15) is a solution to the system of given equations.

Explanation:

Consider the given equations,

4x-y=5 .......(1)

x+y=10 .......(2)

We have to find the ordered pair which is a solution to the system of given equations.

We solve the system by elimination method,

Adding both equation , to eliminate y ,

⇒ 4x - y +( x+y ) = 5+ 10

⇒ 4x - y + x + y = 15

⇒ 5x = 15

⇒ x = 5

Put x = 5 in equation (1) , and solve for y,

We get,

4x - y = 5 ⇒ 4(5) - y = 5 ⇒ y = 20 - 5 ⇒ y = 15

Thus, the ordered pair ( 5, 15) is a solution to the system of given equations.