System of Two Equations: Substitution Method

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Equation (1):    X   +   Y   =             

Equation (2):    X   +   Y   =             

               
               
               
               
               

Equation (1):     3X+4Y = 12


Equation (2):     2X - 5Y = 10


Next we will solve Equation (1) for y:

Equation (1):     3X+4Y = 12

3X - 3X+4Y = 12-3X

4Y = 12-3X

Y = 3 - (3/4)X              divide both sides by 4


Next we substitute the expression 3 - (3/4)X into Equation (2):

Equation (2):     2X - 5Y = 10

2X - 5[3 - (3/4)X] = 10

2X-15+(15/4)X = 10

(23/4)X-15 = 10             combining x terms

(23/4)X-15 + 15 = 10 + 15             add 15 to both sides

(23/4)X = 25

x = 100/23             divide both sides by (23/4)



To find y, we will use : Y = 3 - (3/4)X

Y = 3 - (3/4)(100/23)              replace X with 100/23

Y = -6/23



Solution is {(100/23, -6/23)}



The two lines intersect at one point.
There is one solution.
The system of equations is said to be 'consistent'.

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Absolute Value and Vertical Bars:

For each absolute value expression, make sure that a matching pair of vertical bars are used.
When vertical bars are used to denote absolute value, this calculator is not designed to handle
the case of absolute value expression nested inside another absolute value expression because it's too
ambiguous to interpret user's intention. For a function like f(x) = | 2 + |x + 3| - x |, use "Abs".
f(x) = | 2 + |x + 3| - x | can be input as f(x) = Abs(2 + Abs(x+3) - x).

Links to other pages:

Instruction Manual on how to use graphing calculator

Scientific Calculator

Graphing Calculator with One Function

Graphing Calculator with Two Functions

Graphing Calculator with Three Functions

Graphing Calculator with Four Functions

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