Linear Equations and Systems of Equations Review

Comprehensive review flashcards covering linear equations, slope-intercept form, real-world intercept and slope interpretation, and solving systems of equations by graphing, substitution, and elimination.

When rewriting the equation $2x + y = 7$ in slope-intercept form ($y = mx + b$), the resulting equation is __________.

$$y = -2x + 7$$

When converted to slope-intercept form, the linear equation $3x + 4y = 12$ has a slope of __________.

$$-\frac{3}{4}$$

The equation $5x - 2y = 10$ rewritten in slope-intercept form is $y = \frac{5}{2}x - 5$, which has a y-intercept of __________.

$$-5$$

In a scenario where a water tank is being drained, the graph's x-intercept of $12$ indicates that it takes __________ to completely drain the tank.

$$12\text{ minutes}$$

In the water tank draining problem, the y-intercept of $60$ represents an initial volume of __________ in the tank.

$$60\text{ gallons}$$

For Sam's drive home modeled by the equation $y = -60x + 240$, the slope of $-60$ represents driving at a rate of __________ toward home.

$$60\text{ miles per hour}$$

On the club's T-shirt fundraising profit graph, a y-intercept of $-200$ indicates that the club started __________.

$$\$200\text{ in debt}$$

Gym A charges a $\$30$ fee plus $\$20$ per month, while Gym B charges a $\$10$ fee plus $\$30$ per month; the total cost for both gyms will be identical after __________ months.

$$2$$

Scott begins with $\$120$ and spends $\$15$ per week, whereas Ben begins with $\$20$ and saves $\$10$ per week; both will have the same amount of money after __________ weeks.

$$4$$

Maria buys $7$ total baked goods for $\$18$, where cookies cost $\$2$ each and muffins cost $\$3$ each; solving the system reveals that she purchased __________ cookies.

$$3$$

For an ordered pair to be considered a solution to a system of equations, substituting its coordinates must make __________ of the equations true.

$$\text{both}$$

Substituting the ordered pair $(4, -1)$ into the system $2x - y = 8$ and $x + y = 3$ shows that $(4, -1)$ is __________ a solution to the system.

$$\text{not}$$

The solution obtained by graphing the system of equations $y = x + 1$ and $y = -2x + 4$ is the intersection point __________.

$$(1, 2)$$

Graphing the system $2x + y = 2$ and $y = x - 4$ yields an intersection point and solution of __________.

$$(2, -2)$$

Using substitution to solve the system $2x + y = 8$ and $y = 3x - 2$ results in an x-value of __________.

$$2$$

Adding the equations in the system $5x + 2y = 16$ and $3x - 2y = 0$ to eliminate the y-variable produces the solution ordered pair __________.

$$(2, 3)$$

Solving the system of linear equations $2x + y = 11$ and $3x - 4y = 11$ using elimination gives the ordered pair solution __________.

$$(5, 1)$$

For the linear equation $3x + 4y = 24$, setting $y = 0$ gives an x-intercept of __________.

$$(8, 0)$$

If a tutor's charges are represented by the equation $y = 25x + 15$, the slope of $25$ means the rate is __________.

$$\$25\text{ per hour}$$

In the pool drainage equation $y = -25x + 200$, the slope of $-25$ means that water is being lost at a rate of __________.

$$25\text{ gallons per hour}$$

On Jordan's savings graph showing an increase of $\$10$ per week starting from $\$20$, the y-intercept is __________.

$$20$$

In Step 1 of solving a system by elimination, one aligns like terms and, if necessary, multiplies one or both equations by a constant to obtain __________.

$$\text{opposite terms}$$

In Step 2 of solving by elimination, the aligned equations are added together to __________ one variable.

$$\text{eliminate}$$

In Step 3 of solving by elimination, the solved variable is substituted back into an original equation to find the other variable, expressing the final solution as an __________.

$$\text{ordered pair}$$