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What is the ordered pair for the two equations 3x plus 5y equals 44 and 8x-7y equals -25?
Wiki User
∙ 10y ago
3x+5y=44
8x-7y=-25
Multiply the first equation by 7 and the second by 5.
21x+35y=308
40x-35y=-125
Put them together.
61x=183
x=3
Substitute this back into either equation.
3(3)+5y=44
9+5y=44
5y=35
y=7
To check put both into the other equation.
8(3)-7(7)=-25
24-49=-25
-25=-25 Yeah!
Wiki User
∙ 10y ago
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Plug your ordered pair into both of your equations to see if you get they work.
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What does it mean both algebraically and graphically when an ordered pair is a solution to a system of two linear equations?
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.
What is an ordered pair that makes all equations in a system true?
That would be the "solution" to the set of equations.
