Question

Solve the system of equations:

Answer 1

Answer:

(2,2)

Step-by-step explanation:

2x+3y=10

x−2y=−2

​In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

2x+3y=10,x−2y=−2

To make 2x and x equal, multiply all terms on each side of the first equation by 1 and all terms on each side of the second by 2.

2x+3y=10,2x+2(−2)y=2(−2)

Simplify.

2x+3y=10,2x−4y=−4

Subtract 2x−4y=−4 from 2x+3y=10 by subtracting like terms on each side of the equal sign.

2x−2x+3y+4y=10+4

Add 2x to −2x. Terms 2x and −2x cancel out, leaving an equation with only one variable that can be solved.

3y+4y=10+4

Add 3y to 4y.

7y=10+4

Add 10 to 4.

7y=14

Divide both sides by 7.

y=2

Substitute 2 for y in x−2y=−2. Because the resulting equation contains only one variable, you can solve for x directly.

x−2×2=−2

Multiply −2 times 2.

x−4=−2

Add 4 to both sides of the equation.

x=2

The system is now solved.

x=2,y=2

Correct choice is D) 2,2