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Which equation does the graph of the systems of equations solve?

2 linear graphs. They intersect at 1,2

x + 4 = −2x − 1
x + 2 = −3x + 1
−x + 3 = 3x − 1
x + 3 = 2x − 1

User Fpunkt
by
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2 Answers

3 votes

Answer:

The correct option is 3.

Explanation:

It is given that two linear graphs intersect at (1,2). It means the solution of both lines is x=1 and y=2.

The equation which is satisfied by x=1 will be the required equation.

In option (1),


x+4=-2x-1

Substitute x=1.


(1)+4=-2(1)-1


5\\eq -3

Option 1 is incorrect.

In option (2),


x+2=-3x+1

Substitute x=1.


(1)+2=-3(1)+1


3\\eq -2

Option 2 is incorrect.

In option (3),


-x+3=3x-1

Substitute x=1.


-(1)+3=3(1)-1


2=2

Option 3 is correct.

In option (1),


x+3=2x-1

Substitute x=1.


(1)+3=2(1)-1


4\\eq 1

Option 4 is incorrect.

Therefore the correct option is 3.

User Kshitij Banerjee
by
8.3k points
3 votes
We substitute the point of intesection (1, 2) into the given options to see that only -x + 3 = 3x - 1 satisfies the graphs.
i.e. -x + 3 = -1 + 3 = 2
3x - 1 = 3(1) - 1 = 3 - 1 = 2.
User Inki
by
8.3k points