Mathematics, 23.10.2019 05:20, kbelizaire6

Given the system of equations, what is the solution?

x + 3y = 5
x - 3y = -1

{(-4, -3)}
{(2, 1)}
{(-2, 3)}

Answers: 2

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answered: asialuv

Given the system of equations, what is the solution?

x + 3y = 5

x - 3y = -1

The answer is {(2, 1)}

x=2 and y=1

Step-by-step explanation:

We can find the solution in two ways,the first way is by term elimination the equations:

$x+3y=5 (1)\\x-3y=-1 (2)\\________\\$

2x=4 (3)

We can find x with the equation (3)

$x=\frac{4}{2}\\x=2$

Now we can replace x=2 in the equation (1) to find y

$x+3y=5 (1)\\2+3y=5\\3y=5-2\\3y=3\\y=\frac{3}{3}\\y=1$

Now, we have found x and y

x=2

y=1

The second way is clearing x from equation 1

$x+3y=5\\x=5-3y (4)$

Now, we can replace x=5-3y in the equation (2)

$x-3y=-1 (2)\\(5-3y)-3y=-1\\5-6y=-1\\-6y=-6\\y=\frac{-6}{-6} \\y=1$

Now, we can replace y=1 in the equation (1), (2) or (4) to find x

We will use the equation (1)

$x+3y=5\\x+3(1)=5\\x+3=5\\x=5-3\\x=2$

We have verified that by the two forms x = 2 and y = 1

answered: Guest

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answered: Guest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.