Question

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

3y + x = 6
2y − x = 9

Which statement is true about the coordinates of the point that is the solution to the system of equations? (5 points)



Hint: Add the two equations and use inverse operations. When you have your y-value, plug it into any of the original equations to find your x-value.

a
It is (−6, 4) and lies on both lines.

b
It is (−3, 3) and lies on both lines.

Answer 1

b) It is (-3, 3) and lies on both lines.

Step-by-Step Explanation;

Lets solve using Elimination Method;

=> 3y + x = 6 (Eq. 1)
=> 2y - x = 9 (Eq. 2)

Adding Eq. 1 and 2, we get :-

5y = 15 (‘x’ gets Eliminated)
=> y = 15/5 = 3

Therefore, y = 3

Substitute value of ‘y’ in Eq. 1 :-

3y + x = 6
3(3) + x = 6
9 + x = 6
x = 6 - 9
=> x = -3

Therefore, x = -3

This can be written as an ordered pair as (-3, 3) where the ‘x’ coordinate is the value if x and the y coordinate is the value of ‘y’.