QuestionSolve the system of equations: $3x + 5y = 1$ and $-x - \frac{5}{3}y = -\frac{1}{3}$ .

Studdy Solution

STEP 1

Assumptions1. We are given two linear equations in two variables, x and y. . The equations are $3x +5y =1$ $-x - \frac{5}{3}y = -\frac{1}{3}$ 3. We need to find the values of x and y that satisfy both equations.

STEP 2

We can solve the system of equations using substitution or elimination method. Here, we will use the elimination method.First, we need to make the coefficients of y in both equations the same. To do this, we multiply the second equation by.
$(-x - \frac{5}{}y) =(-\frac{1}{})$

STEP 3

implify the equation obtained in2.
$-3x -5y = -1$

STEP 4

Now, we have two equations with the same coefficients for y.
$3x +y =1$ $-3x -y = -1$ We can add these two equations to eliminate y.

STEP 5

Add the two equations.
$(3x +5y) + (-3x -5y) =1 + (-1)$

STEP 6

implify the equation obtained in5.
$0 =0$ This means that the two equations are dependent and have infinite solutions. The solution is any point on the line represented by either equation.

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QuestionSolve the system of equations: $3x + 5y = 1$ and $-x - \frac{5}{3}y = -\frac{1}{3}$ .

Studdy Solution

STEP 1

Assumptions1. We are given two linear equations in two variables, x and y. . The equations are $3x +5y =1$ $-x - \frac{5}{3}y = -\frac{1}{3}$ 3. We need to find the values of x and y that satisfy both equations.

STEP 2

We can solve the system of equations using substitution or elimination method. Here, we will use the elimination method.First, we need to make the coefficients of y in both equations the same. To do this, we multiply the second equation by.
$(-x - \frac{5}{}y) =(-\frac{1}{})$

STEP 3

implify the equation obtained in2.
$-3x -5y = -1$

STEP 4

Now, we have two equations with the same coefficients for y.
$3x +y =1$ $-3x -y = -1$ We can add these two equations to eliminate y.

STEP 5

Add the two equations.
$(3x +5y) + (-3x -5y) =1 + (-1)$

STEP 6

implify the equation obtained in5.
$0 =0$ This means that the two equations are dependent and have infinite solutions. The solution is any point on the line represented by either equation.

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QuestionSolve the system of equations: 3x+5y=13x + 5y = 13x+5y=1 and −x−53y=−13-x - \frac{5}{3}y = -\frac{1}{3}−x−35​y=−31​.

Studdy Solution

STEP 1

Assumptions1. We are given two linear equations in two variables, x and y. . The equations are 3x+5y=13x +5y =13x+5y=1 −x−53y=−13-x - \frac{5}{3}y = -\frac{1}{3}−x−35​y=−31​3. We need to find the values of x and y that satisfy both equations.

STEP 2

STEP 3

implify the equation obtained in2.−3x−5y=−1-3x -5y = -1−3x−5y=−1

STEP 4

Now, we have two equations with the same coefficients for y.3x+y=13x +y =13x+y=1−3x−y=−1-3x -y = -1−3x−y=−1We can add these two equations to eliminate y.

STEP 5

Add the two equations.(3x+5y)+(−3x−5y)=1+(−1)(3x +5y) + (-3x -5y) =1 + (-1)(3x+5y)+(−3x−5y)=1+(−1)

STEP 6

implify the equation obtained in5.0=00 =00=0This means that the two equations are dependent and have infinite solutions. The solution is any point on the line represented by either equation.

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QuestionSolve the system of equations: $3x + 5y = 1$ and $-x - \frac{5}{3}y = -\frac{1}{3}$ .

Assumptions1. We are given two linear equations in two variables, x and y. . The equations are $3x +5y =1$ $-x - \frac{5}{3}y = -\frac{1}{3}$ 3. We need to find the values of x and y that satisfy both equations.

implify the equation obtained in2.
$-3x -5y = -1$

Now, we have two equations with the same coefficients for y.
$3x +y =1$ $-3x -y = -1$ We can add these two equations to eliminate y.

Add the two equations.
$(3x +5y) + (-3x -5y) =1 + (-1)$

implify the equation obtained in5.
$0 =0$ This means that the two equations are dependent and have infinite solutions. The solution is any point on the line represented by either equation.