Question

the graphs for -6x + y = 17 and 5x - 2y = -6 intersect at ____. the graphs for -7x + 10y = -20 and 10x - 10y = -10 intersect at ____. what ordered pair makes each statement true? drag the correct ordered pair to each statement. click or tap the reset button to start over. \\(\left(-3\frac{1}{3}, -13\frac{1}{3}\
ight)\\) \\((-4, -7)\\) \\(\left(-5\frac{5}{7}, -17\frac{2}{7}\
ight)\\) \\((-7, -4)\\) \\((-9, -10)\\) \\((-10, -9)\\)

Explanation:

Step1: Solve first system of equations

We have the system:

$$\begin{cases} -6x + y = 17 \\ 5x - 2y = -6 \end{cases}$$

From first equation, express $y$: $y = 6x + 17$
Substitute into second equation:
$5x - 2(6x + 17) = -6$
$5x - 12x - 34 = -6$
$-7x = 28$
$x = -4$
Substitute $x=-4$ back to $y=6x+17$:
$y = 6(-4) + 17 = -24 + 17 = -7$

Step2: Solve second system of equations

We have the system:

$$\begin{cases} -7x + 10y = -20 \\ 10x - 10y = -10 \end{cases}$$

Add the two equations to eliminate $y$:
$(-7x + 10y) + (10x - 10y) = -20 + (-10)$
$3x = -30$
$x = -10$
Substitute $x=-10$ into second equation:
$10(-10) - 10y = -10$
$-100 -10y = -10$
$-10y = 90$
$y = -9$

Answer:

The graphs for $-6x + y = 17$ and $5x - 2y = -6$ intersect at $\boldsymbol{(-4, -7)}$.
The graphs for $-7x + 10y = -20$ and $10x - 10y = -10$ intersect at $\boldsymbol{(-10, -9)}$.