Question

Решить системы. X+y=2 5x+80y=130. И 5s-7t=18,9 s+4t=_8,1

Answer 1

Пошаговое объяснение:

$\left \{ {{x+y=2} \atop {5x+8y=130}} \right. \\ \\ \left \{ {{x=2-y} \atop {5x+8y=130}} \right. \\ \\ 5*(2-y)+8y=130\\10-5y+8y=130\\3y=120\\y=40\\x=2-40=-38$

Ответ : х=-38; у=40

$\left \{ {{5s-7t=18,9} \atop {s+4t=-8,1}} \right. \\ \\ s=-8,1-4t\\5*(-8,1-4t)-7t=18,9\\-40,5-20t-7t=18,9\\-27t=18,9+40,5\\-27t=59,4\\t=-2,2\\s=-8,1-4*(-2,2)=0.7$

Ответ: s=0,7; t=-2,2

Answer 2

Let's solve the systems of equations one by one:

1. Solving the system: $x + y = 2$ $5x + 80y = 130$

We can use the method of substitution or elimination. I'll use the elimination method.

Step 1: Multiply the first equation by 5 to make the coefficients of x in both equations equal. $5(x + y) = 5 \times 2 \Rightarrow 5x + 5y = 10$

Step 2: Subtract the second equation from the equation obtained in Step 1 to eliminate the x term. $(5x + 5y) - (5x + 80y) = 10 - 130$ $5y - 80y = -120$ $-75y = -120$

Step 3: Solve for y. $y = \frac{-120}{-75} = \frac{8}{5}$

Step 4: Substitute the value of y back into the first equation to solve for x. $x + \frac{8}{5} = 2$ $x = 2 - \frac{8}{5}$ $x = \frac{2}{5}$

So the solution to the first system of equations is $x = \frac{2}{5}$ and $y = \frac{8}{5}$.

2. Solving the system: $5s - 7t = 18$ $9s + 4t = -8$

Again, we can use either substitution or elimination method. I'll use the elimination method.

Step 1: Multiply the first equation by 9 and the second equation by 5 to make the coefficients of s in both equations equal.

$9(5s - 7t) = 9 \times 18 \Rightarrow 45s - 63t = 162$ $5(9s + 4t) = 5 \times -8 \Rightarrow 45s + 20t = -40$

Step 2: Add the two equations to eliminate the s term.

$(45s - 63t) + (45s + 20t) = 162 - 40$ $90s - 43t = 122$

Step 3: Now we have a linear equation in two variables (s and t).

To solve for s, let's express s in terms of t from the equation $90s - 43t = 122$:

$90s = 43t + 122$ $s = \frac{43t + 122}{90}$

Step 4: Substitute the expression for s in terms of t into one of the original equations to solve for t. Let's use the first equation:

$5s - 7t = 18$ $5\left(\frac{43t + 122}{90}\right) - 7t = 18$ $\frac{43t + 122}{18} - 7t = 18$ $43t + 122 - 126t = 3240$

Step 5: Solve for t.

$-83t = 3240 - 122$ $-83t = 3118$ $t = \frac{3118}{-83}$ $t \approx -37.57$

Step 6: Substitute the value of t back into the expression for s to solve for s.

$s = \frac{43t + 122}{90}$ $s = \frac{43(-37.57) + 122}{90}$ $s \approx -7.74$

So the solution to the second system of equations is $s \approx -7.74$ and $t \approx -37.57$.