Question

2x+3y=19 // 6x+2y=22​

Answer 1

Answer:

(2, 5 )

Step-by-step explanation:

Given the 2 equations

2x + 3y = 19 → (1)

6x + 2y = 22 → (2)

Multiplying (1) by - 3 and adding to (2) will eliminate the x- term

- 6x - 9y = - 57 → (3)

Add (2) and (3) term by term to eliminate x

0 - 7y = - 35

- 7y = - 35 ( divide both sides by - 7 )

y = 5

Substitute y = 5 into either of the 2 equations and solve for x

Substituting into (1)

2x + 3(5) = 19

2x + 15 = 19 ( subtract 15 from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

solution is (2, 5 )

Answer 2

Answer:

$x=2\\y=5$

Step-by-step explanation:

Multiply both sides of the equation by a coefficient:  $\left \{ {{3(2x+3y)=19x3} \atop {6x+2y=22}} \right.$

Apply Multiplicative Distribution Law: $\left \{ {{6x+9y=19x3} \atop {6x+2y=22}} \right.$

Calculate the first two terms: $\left \{ {{6x+9y=57} \atop {6x+2y=22}} \right.$

Subtract the two equations: $6x+9y-(6x+2y)=57-22$

Remove parentheses: $6x+9y-6x-2y=57-22$

Cancel the unknown variables: $9y-2y=57-22$

Combine like terms: $7y=57-22$

Calculate the sum or difference: $7y=35$

Reduce the greatest common factor on both sides of the equation: $y=5$

Substitute one unknown quantity into the elimination: $6x+9x5=57$

Reduce the greatest common factor on both sides of the equation: $2x+3x5=19$

Rearrange unknown terms to the left side of the equation: $2x=19-3$·$5$

Calculate the product or quotient: $2x=19-15$

Calculate the sum or difference: $2x=4$

Reduce the greatest common factor on both sides of the equation: $x=2$

Write the solution set of the equations: $\left \{ {{x=2} \atop {y=5}} \right.$

Answer: $\left \{ {{x=2} \atop {y=5}} \right.$