Solve each system of equations
5x- 2y = 3
2x + 5y = 7 Ordered pair

(1, 1)

Step-by-step explanation:

Solve the System of Equations

5x − 2y = 3

2x + 5y = 7

Solve for x in the first equation.

x =  3/5 + 2y /5

2x + 5y = 7

Replace all occurrences of x with   3/5 +2y /5  in each equation.

Replace all occurrences of x in 2x   + 5y   = 7 with   3/5 + 2y/5

 2 ( (3/5) +  (2y/5))+ 5y = 7

 x =  3/5 + 2y /5

Simplify 2((3/5)+(2y/5)) +5

6 + 29y  = 7  ⋅(5)

x = (3/5)+(2y/5)

Solve for y in the first equation.

Multiply both sides of the equation by 5.

6 + 29y = 7 ⋅ (5)

x = (3/5)+(2y/5)

 Remove parentheses.

6 + 29y = 7 ⋅ (5)

x = (3/5)+(2y/5)

Multiply 7 by 5.

6 + 29y = 35

x = (3/5)+(2y/5)

Move all terms not containing y to the right side of the equation.

Subtract 6 from both sides of the equation.

29y = 35 − 6

x = (3/5)+(2y/5)

Subtract 6 from 35.

29y = 29

x = (3/5)+(2y/5)

Divide each term by 29 and simplify.

Divide each term in 29y = 29 by 29.

29y/29  = 29/29

x = (3/5)+(2y/5)

Cancel the common factor of 29.

y = 29 /29

x = (3/5)+(2y/5)

Divide 29 by 29.

 y = 1

x = (3/5)+(2y/5)

Replace all occurrences of y with 1 in each equation.

Replace all occurrences of y in x = (3/5)+(2y/5) with 1.

  x = (3/5)+(2(1)/5)3

 y = 1

Simplify

x = (3/5)+(2(1)/5)3  

y = 1

x = 1

y = 1

The solution to the system is the complete set of ordered pairs that are valid solutions.

(1, 1)

The result can be shown in multiple forms.

Point Form:

(1, 1)

Equation Form:

x = 1, y = 1

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

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step-by-step explanation: