Question

1. solve: \\(\

$$\begin{cases} y = 6x \\\\ 4x + y = 7 \\end{cases}$$

\\) 2. solve: \\(\

$$\begin{cases} y = 3x \\\\ x = -2y + 70 \\end{cases}$$

\\)

Explanation:

System 1:

Step1: Substitute $y=6x$ into the second equation

$4x + 6x = 7$

Step2: Combine like terms

$10x = 7$

Step3: Solve for $x$

$x = \frac{7}{10} = 0.7$

Step4: Substitute $x$ back to find $y$

$y = 6 \times \frac{7}{10} = \frac{42}{10} = 4.2$

System 2:

Step1: Substitute $y=3x$ into the second equation

$x = -2(3x) + 70$

Step2: Expand the right-hand side

$x = -6x + 70$

Step3: Isolate $x$ terms

$x + 6x = 70$
$7x = 70$

Step4: Solve for $x$

$x = 10$

Step5: Substitute $x$ back to find $y$

$y = 3 \times 10 = 30$

Answer:

1. $x = \frac{7}{10}$, $y = \frac{21}{5}$ (or $x=0.7$, $y=4.2$)
2. $x = 10$, $y = 30$