Question

3x - y = 4
x + 2y = 6

Answer 1

(2,2)

Explanation:

Since the y's already have different signs, you can multiply the top equation by 2 and eliminate the y's. You may instead multiply the bottom equation by -3 and eliminate the x's. Either way, solve for the variable that is left. Plug that answer back into either equation and solve for the other variable. The answer is (2,2).

3x−y=4;x+2y=6

Step: Solve3x−y=4for y:

3x−y+−3x=4+−3x(Add -3x to both sides)

−y=−3x+4

−y

−1

=

−3x+4

−1

(Divide both sides by -1)

y=3x−4

Step: Substitute3x−4foryinx+2y=6:

x+2y=6

x+2(3x−4)=6

7x−8=6(Simplify both sides of the equation)

7x−8+8=6+8(Add 8 to both sides)

7x=14

7x

7

=

14

7

(Divide both sides by 7)

x=2

Step: Substitute2forxiny=3x−4:

y=3x−4

y=(3)(2)−4

y=2(Simplify both sides of the equation)

Answer:

x=2 and y=2

Answer 2

To solve this you can multiply the second equation by to get

3x+6y =18

Then you can subtract it by the first equation to get

7y= 14
And get y= 2
Then you plug in y to one of the equations to find that x=2