Q: What is the ordered pair the is th solution to these equations x equals 5y and 2x - 3y equals 14?

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The ordered pair is (1, 3).

If an ordered pair is a solution to a system of linear equations, then algebraically it returns the same values when substituted appropriately into the x and y variables in each equation. For a very basic example: (0,0) satisfies the linear system of equations given by y=x and y=-2x By substituting in x=0 into both equations, the following is obtained: y=(0) and y=-2(0)=0 x=0 returns y=0 for both equations, which satisfies the ordered pair (0,0). This means that if an ordered pair is a solution to a system of equations, the x of that ordered pair returns the same y for all equations in the system. Graphically, this means that all equations in the system intersect at that point. This makes sense because an x value returns the same y value at that ordered pair, meaning all equations would have the same value at the x-coordinate of the ordered pair. The ordered pair specifies an intersection point of the equations.

The pair of equations: x + y = 1 and x + y = 3 have no solution. If any ordered pair (x,y) satisfies the first equation it cannot satisfy the second, and conversely. The two equations are said to be inconsistent.

There are an infinite number of ordered pairs that satisfy the equation.

It's an inconsistent pair of equations, for which there is no solution.

Related questions

7

Plug your ordered pair into both of your equations to see if you get they work.

y=(-1) x=(2)

Always. Every ordered pair is the solution to infinitely many equations.

The ordered pair is (1, 3).

That would be the "solution" to the set of equations.

(0,7)

an ordered pair that makes both equations true

The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.

Tell whether the ordered pair (5, -5) is a solution of the system

x = -3/5 and y = -24/5

If an ordered pair is a solution to a system of linear equations, then algebraically it returns the same values when substituted appropriately into the x and y variables in each equation. For a very basic example: (0,0) satisfies the linear system of equations given by y=x and y=-2x By substituting in x=0 into both equations, the following is obtained: y=(0) and y=-2(0)=0 x=0 returns y=0 for both equations, which satisfies the ordered pair (0,0). This means that if an ordered pair is a solution to a system of equations, the x of that ordered pair returns the same y for all equations in the system. Graphically, this means that all equations in the system intersect at that point. This makes sense because an x value returns the same y value at that ordered pair, meaning all equations would have the same value at the x-coordinate of the ordered pair. The ordered pair specifies an intersection point of the equations.