Exam 4: Systems of Equations

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either? - $y=-\frac{1}{2} x-5$ $3 \mathrm{x}+7 \mathrm{y}=19$

Solve the system of equations using Cramer's rule. - $2 x+5 y=2$ $-7 x-4 y=20$

The Family Fine Arts Center charges $\$ 21$ per adult and $\$ 11$ per senior citizen for its performances. On a recent weekend evening when 465 people paid admission, the total receipts were $\$ 6315$ . How many who paid were senior citizens?

Solve the system of four equations in four unknowns using matrices. - $9 w+8 x-5 y-4 z=19$ $8 w+6 x-8 y-4 z=-2$ $9 \mathrm{w}-8 \mathrm{x}+6 \mathrm{y}+5 \mathrm{z}=-35$ $-5 \mathrm{w}-4 \mathrm{x}+8 \mathrm{y}+9 \mathrm{z}=-1$

Is the ordered pair a solution of the given system of equations? - left parenthesis2commaminus4right parenthesiscomma 3x+y=2 4x+3y=-4

Solve the system by substitution. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $x=-17-5 y$ $-2 \mathrm{x}+4 \mathrm{y}=-22$

Don runs a charity fruit sale, selling boxes of oranges for $\$ 11$ and boxes of grapefruit for $\$ 10$ . If he sold a total of 762 boxes and took in $\$ 8125$ in all, then how many boxes of oranges did he sell?

Why could $(5,-3)$ not be a solution of the system that is graphed?

$6 x-y+8 z=52$ $6 x+9 y-3 z=57$ $6 x-4 y+z=-1$

$5 x-4 y+10 z=-3$ $10 \mathrm{x}+2 \mathrm{y}-15 \mathrm{z}=21$ $15 \mathrm{x}-2 \mathrm{y}+10 \mathrm{z}=0$

Two angles are supplementary. One angle is $52^{\circ}$ less than three times the other. Find the measures of the angles.

Walt made an extra $\$ 7000$ last year from a part- time job. He invested part of the money at $7 \%$ and the rest at $10 \%$ . He made a total of $\$ 580$ in interest. How much was invested at $10 \%$ ?

Is the ordered triple a solution to the given system of equations? - $(-3,-1,4)$ 2x-2y-3z =-16 4x-3y+3z =3 X+y-5z =-24

Solve the system of equations using matrices. - $-2 x+2 y-z=3$ $x+2 y+2 z=15$ $4 \mathrm{x}+\mathrm{y}+\mathrm{z}=18$

Graph the system of inequalities. - $3y + x \geq 0$ $y + 2x \leq 10$ $Y \geq 0$

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $7 x-5 y=20$ $-4 \mathrm{x}+3 \mathrm{y}=-12$

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $x+8 y=51$ $-4 x+7 y=69$

In triangle $A B C$ , the measure of angle $B$ is $68^{\circ}$ more than twice the measure of angle $A$ . The measure of angle $\mathrm{C}$ is $64^{\circ}$ more than that of angle $\mathrm{A}$ . Find the angle measures.

Solve by addition or substitution. - $x+7 y=7$ $4 \mathrm{x}-5 \mathrm{y}=-5$

If the $y$ term is missing in both of two linear equations, the lines are ?