Find the values of a and b so that the linear system has the given solution.

Mathematics

1 answer:

mojhsa [17]2 years ago

3 0

Answer:

<em>The values are a=6, b=8</em>

Step-by-step explanation:

The following system of equations

ax - by = 4

bx - ay = 10

Has the solution x=2, y=1. Substituting:

2a - b = 4 [1]

2b - a = 10 [2]

Multiply [1] by 2:

4a - 2b = 8

Add with [2]:

3a = 18

a = 18/3 = 6

a = 6

From [1]:

2*6 - b = 4

b = 12 - 4

b = 8

The values are a=6, b=8

You might be interested in

What's 2 and 5/10 in standard decimal form

Evgesh-ka [11]

2 5/10 = 2 1/2 = 2.5

4 0

3 years ago

What is an equation of the line that is perpendicular to −x+2y=4 and passes through the point (−2, 1) ?

Elza [17]

Answer:

y=-2x-3

Step-by-step explanation:

Since our equation is in standard form Ax+By=C we must first manipulate the equation so that we have it in the slope-intercept form such that y=mx+b. Therefore:

$-x+2y=4\\2y=x+4\\\\y=\frac{x+4}{2}\\\\y=\frac{1}{2}x+2$

Therefore, our slope is 1/2 and our y-intercept is 2. Now in order to determine a perpendicular line to the one stated above we must then get the negative inverse of our slope meaning $\frac{1}{2}=-2$ (negative reciprocal). Now we must use the point slope formula: