Question

Estimate the solution to the following system of equations by graphing.

3x + 5y = 14
6x - 4y = 9

A.(7/3,-7/2)
B.(-5/2,-7/2)
C.(5/2,4/3)
D.(4/3,5/2)

Answer 1

Answer:

Step-by-step explanation:

Draw the 2 lines of the equations on graph paper.

The coordinates of the point where they cross is the solution

The answer is (5/2, 4/3)

Answer 2

Answer:

C. (5/2, 4/3)

Step-by-step explanation:

The system of equations that are given are:

• $3x + 5y = 14$

• $6x - 4y = 9$

To solve, let's use the substitution method.

• Note: The substitution method for solving two-order systems involves solving one equation using the terms of the other equation.

See Below:

So solving by substitution:

// Solve equation [2] for the variable  x

•  [2]    6x = 4y + 9

•  [2]    x = 2y/3 + 3/2

// Plug this in for variable  x  in equation [1]

•   [1]    3•(2y/3+3/2) + 5y = 14
•   [1]    7y = 19/2
•   [1]    14y = 19

// Solve equation [1] for the variable  y

•   [1]    14y = 19

•   [1]    y = 19/14

// By now we know this much :

•    x = 2y/3+3/2
•    y = 19/14

// Use the  y  value to solve for  x

•    x = (2/3)(19/14)+3/2 = 101/42

Therefore, the solution is:

${x,y} =\frac{101}{42} ,\frac{19}{14}$

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Terms and topics:

• Linear equations with two unknowns
• Solving linear equations by substitution

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Level:

• Algebra l (Pre-algebra concepts)

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