Question 1

Given the system of equations:

$\frac{8}{5}x - y = 6$

$\frac{2}{3}x - \frac{1}{2}y = 7$

What is the solution $(x, y)$ to this system?

Accepted Answer

$(x, y) = (\frac{11}{5}, \frac{32}{5})$

Question 2

When solving a system of equations with fractional coefficients, what is the recommended first step?

Accepted Answer

Multiply each equation by the least common denominator (LCD) to clear fractions.

Question 3

Given the system:

$2x + 3y = 6$

$4x + 3y = 6$

What is the value of $x$ after using the elimination method?

Accepted Answer

$x = 0$

Question 4

After finding $x = 0$ in the previous system, what is the value of $y$?

Accepted Answer

$y = 2$

Question 5

Which of the following is the correct ordered pair solution to the system:

$2x + 3y = 6$

$4x + 3y = 6$

Accepted Answer

$(0, 2)$

Question 6

If you have the equation $3y = -2x - 6$, what is $y$ in terms of $x$?

Accepted Answer

$y = -\frac{2}{3}x - 2$

Question 7

Which method involves combining two equations in a system so that one variable is eliminated?

Accepted Answer

Elimination method

Question 8

What is the slope-intercept form of the equation $3y = -2x - 6$?

Accepted Answer

$y = -\frac{2}{3}x - 2$

Question 9

If you multiply each term in an equation by 10, 100, or 1000, what are you trying to accomplish?

Accepted Answer

Eliminate decimals from the equation

Question 10

Given the system:

$4x + 3y = 7$

$8x - 6y = 6$

What is the first step to solve using elimination?

Accepted Answer

Multiply the second equation by $\frac{1}{2}$ to match the $y$ coefficients

Question 11

After solving the system $4x + 3y = 7$ and $8x - 6y = 6$, what is the value of $y$?

Accepted Answer

$y = \frac{32}{5}$

Question 12

What is the ordered pair solution to the system $4x + 3y = 7$ and $8x - 6y = 6$?

Accepted Answer

$(\frac{11}{5}, \frac{32}{5})$

Question 13

When using the elimination method, what should you do if the coefficients of $y$ are $+3$ and $-6$?

Accepted Answer

Multiply the first equation by 2 to make the coefficients $+6$ and $-6$

Question 14

If you have the system $2x + 3y = 6$ and $4x + 3y = 6$, what is the result after subtracting the first equation from the second?

Accepted Answer

$2x = 0$

Question 15

After finding $x = 0$ in the system $2x + 3y = 6$ and $4x + 3y = 6$, how do you find $y$?

Accepted Answer

Plug $x = 0$ into either equation and solve for $y$

Question 16

What is the slope of the line $y = -\frac{2}{3}x - 2$?

Accepted Answer

$-\frac{2}{3}$

Question 17

Which of the following is a correct step in the substitution method for solving systems of equations?

Accepted Answer

Solve one equation for one variable, then substitute into the other equation

Question 18

If you have the system $3y = -2x - 6$ and $y = \frac{3}{2}x - 2$, what is the solution $(x, y)$?

Accepted Answer

$(x, y) = (0, -2)$

Solving Systems of Linear Equations: Fractions, Elimination, and Substitution Methods 3.1

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