Answered

NEED HELP ASAP!!
(08.01 MC)

The system of equations shown below is graphed on a coordinate grid:

3y + x = 4
2y − x = 6

Which statement is true about the coordinates of the point that is the solution to the system of equations?

It is (−2, 2) and lies on both lines.
It is (−5, 3) and lies on both lines.
It is (−5, 3) and does not lie on either line.
It is (−2, 2) and does not lie on either line.

Answer :

3y+x=4
2y-x=6
Solve x+3y=4 for x
Add -3y to both sides
x+3y-3y=4-3y
x=-3y+4
Substitute -3y+4 for x in -x+2y=6
-x+2y=6
-(-3y+4)+2y=6
Simplify both sides of the equation
5y-4=6
Add 4 to both sides
5y-4+4=6+4
5y=10
Divide both sides by 5
5y/5=10/5
y=2
Substitute 2 for y in x=-3y+4
x=-3y+4
x=(-3)(2)+4
x= -6+4
x= -2
Answer : x=-2 and y=2
The answer is A
it is (-2,2) and lies on both lines

I hope that's help !
AmeliaGAponte

Let's solve your system by substitution.

3y+x=4;2y−x=6

Rewrite equations:

x+3y=4;−x+2y=6

Step: Solvex+3y=4for x:

x+3y=4

x+3y+−3y=4+−3y(Add -3y to both sides)

x=−3y+4

Step: Substitute−3y+4forxin−x+2y=6:

−x+2y=6

−(−3y+4)+2y=6

5y−4=6(Simplify both sides of the equation)

5y−4+4=6+4(Add 4 to both sides)

5y=10

5y

5

=

10

5

(Divide both sides by 5)

y=2

Step: Substitute2foryinx=−3y+4:

x=−3y+4

x=(−3)(2)+4

x=−2(Simplify both sides of the equation)

Answer:

x=−2 and y=2

Your line would also lay on both lines so the answer would be the first one: It is (−2, 2) and lies on both lines.

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