4x + 3y = 17
5x – 2y = 4
​

x=2

y=3

Step-by-step explanation:

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.

4x+3y=17,5x−2y=4

To make 4x and 5x equal, multiply all terms on each side of the first equation by 5 and all terms on each side of the second by 4.

5×4x+5×3y=5×17,4×5x+4(−2)y=4×4

Simplify.

20x+15y=85,20x−8y=16

Subtract 20x−8y=16 from 20x+15y=85 by subtracting like terms on each side of the equal sign.

20x−20x+15y+8y=85−16

Add 20x to −20x. Terms 20x and −20x cancel out, leaving an equation with only one variable that can be solved.

15y+8y=85−16

Add 15y to 8y.

23y=85−16

Add 85 to −16.

23y=69

Divide both sides by 23.

y=3

Substitute 3 for y in 5x−2y=4. Because the resulting equation contains only one variable, you can solve for x directly.

5x−2×3=4

Multiply −2 times 3.

5x−6=4

Add 6 to both sides of the equation.

5x=10

Divide both sides by 5.

x=2

The system is now solved.

x=2,y=3

answer: 1 + 1 = 11

step-by-step explanation: