How many solutions does the following system of equations have?
y = x - 2
y = -x + 2
one solution
no solutions
two solutions
infinitely many solutions

One solution

Step-by-step explanation:

Since y = x - 2 and y = -x + 2 are both linear equations (create straight lines when graphed, or do not have exponents algebraically), this is a linear system of equations.

A solution to a system of equations means the point of intersection, or meeting point when the lines are graphed.

Situations for linear systems where you would have each number of solutions:

No solutions - when the lines are parallel to each other. You know two lines are parallel when they have the same slope. Remember parallel lines means lines that never meet. If lines never meet, they can't have a solution.

Infinitely many solutions - when the lines are the same. When you graph equivalent equations, you would end up drawing one line on top of the other.

Two solutions - impossible in linear systems. Since straight lines do not curve, they could not have two solutions. (If you have a straight line and a circle, you could have two solutions.)

One solution - all other situations. When the slopes are different and the equations are not equivalent, there will be one solution.

What are the slopes in the equations?

These equations are written in slope-intercept form y = mx + b

'm' represents the slope

'b' represents the y-intercept (when the line hits the y-axis)

'x' and 'y' represent points on the line

In y = x - 2 , m = 1

In y = -x + 2, m = -1

Since the slopes are different, we know the answer is not "no solutions".

Check if the equations are equivalent.

Choose a random value for x. If both sides are equal, then they are equivalent.

y = y        Substitute each 'y' with the two equations

x - 2 = -x + 2        Substitute 'x' for 3

(3) - 2 = -(3) + 2        Simplify both sides

1 = -1        The numbers are different

LS ≠ RS        Left side does not equal to right side

The equations are not equivalent, so the answer is not "infinitely many solutions".

Linear equations cannot have two solutions.

Therefore the system of equations has one solution.

1/3

step-by-step explanation:

to find this, you can divide 12 by 4 which is 3 or you can multiply 4 until you reach 12 (4x3=12). both should give you 3, meaning theres three times less bananas than there are oranges.