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3 years ago

x + 3y = 7 x - 3y = 1 Solve the system of equations. A) x = 4, y = 1 B) x = 1, y = 4 C) x = - 2 3 , y = 3 D) x = 3, y = - 2 3

2 answers:

6 0

X+3y=7
x-3y=1
add them together

x+3y=7
x-3y=1 +
2x+0y=8

2x=8
divide 2
x=4
subsitute
x+3y=7
4+3y=7
subtract 4
3y=3
divid 3
y=1

x=4
y=1

answer is A

Bumek [7]3 years ago

6 0

X + 3y = 7
x - 3y = 1

x + 3y = 7
- 3y -3y

x = 7 - 3y

x - 3y = 1
7 - 3y - 3y = 1
7 -6y = 1
-7 -7

-6y = -6
y = 1

Now solve for x

X + 3y = 7
x + 3 = 7
x = 4

Now we have our values:-
x = 4 and y = 1

Answer: A) x = 4, y = 1

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what is the slope,y intercept ,are the lines the same intersecting ,or parallel? What are the number of solutions? Classificatio

ohaa [14]

Answer:

For equation: y = 2x + 3 , 2x - y = 5 There is no solution to this system of equations.
For equation: y = 2x + 3 , 2x - y = 5 There is one solution to the system of equations.
For equation: y = x + 4 , y = x + 4 There are infinite solutions to the system.

Step-by-step explanation:

The equation of straight line is written as y = m x + c where 'm' is slope.
y - intercept of line is value which intersect the point on y-axis.
To find y -intercept , put x = 0 in equation.
If slope of two lines are equal then lines are parallel.
If the lines are not parallel, they will always intersect

For equation: y = 2x + 3 , 2x - y = 5

Compare equation y = 2x + 3 with y = m x + c then we get slope 'm' is 2.

Now, put x = 0 in y = 2x + 3 to get y-intercept

y = 2(0)+ 3

y = 0 + 3

y = 3

so, the y-intercept is 3 .

Re-write this equation 2x - y = 5 in the slope intercept form;

Subtract 2x from both the sides of 2x - y = 5

2x - y - 2x = 5 - 2x

- y = - 2x + 5

Multiply both the sides by '-1'

y = 2x - 5

so, when we compare above equation with y = m x + c then we get slope 'm' is 2 .

Now, put x = 0 in y = 2x - 5 to get y-intercept

y = 2(0) - 5

y = 0 - 5

y = - 5

so, the y-intercept is - 5 .

Equation y = 2x + 3 and 2x - y = 5 are parallel (since there slope are equal 'm = 2').

There is no solution to this system of equations.

For equation: 3x - y = 5 , 2x + y = -3

Re-write this equation 3x - y = 5 in the slope intercept form;

Subtract 3x from both the sides of 3x - y = 5

3x - y - 3x = 5 - 3x

- y = - 3x + 5

Multiply both the sides by '-1'

y = 3x - 5

so, when we compare above equation with y = m x + c then we get slope 'm' is 3 .

Now, put x = 0 in y = 3x - 5 to get y-intercept

y = 3(0) - 5

y = 0 - 5

y = - 5

so, the y-intercept is - 5 .

Re-write this equation 2x + y = -3 in the slope intercept form;

Subtract 2x from both the sides of 2x + y = -3

2x - y - 2x = -3 - 2x

- y = - 2x - 3

Multiply both the sides by '-1'

y = 2x + 3

so, when we compare above equation with y = m x + c then we get slope 'm' is 2 .

Now, put x = 0 in y = 2x + 3 to get y-intercept

y = 2(0) + 3

y = 0 + 3

y = 3

so, the y-intercept is 3 .

Equation 3x - y = 5 and 2x + y = -3 are intersecting lines (since their slope are not equal).

There is one solution to the system of equations (since the lines are intersect).

For equation: y = x + 4 , y = x + 4

Compare equation y = x + 4 with y = m x + c then we get slope 'm' is 1.

Now, put x = 0 in y = x + 4 to get y-intercept

y = 0+ 4

y = 4

so, the y-intercept is 4 .

since equation of line are same therefore slopes are also equal

Equation y = x + 4 and y = x + 4 are parallel lines.

There are infinite solutions to the system. ( Since equivalent equation)

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