Jacqueline Said:

Please help me solve these linear equations using substitution!?

We Answered:

x = y - 4
3x + y = 12

Substitute x with y - 4 in the second equation.
3x + y = 12
3(y - 4) + y = 12

Distribute.
3(y) + 3(-4) + y = 12
3y - 12 + y = 12
4y - 12 = 12

Add 12 to both sides.
4y - 12 + 12 = 12 + 12
4y = 24

Divide both sides by 4.
4y / 4 = 24 / 4
y = 6

Plug this into the first equation to find x.
x = y - 4
x = 6 - 4
x = 2

ANSWER: (2, 6)

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y - 5 = x
4x - y = 4

Substitute x with y - 5 in the second equation.
4x - y = 4
4(y - 5) - y = 4

Distribute.
4(y) + 4(-5) - y = 4
4y - 20 - y = 4
3y - 20 = 4

Add 20 to both sides.
3y - 20 + 20 = 4 + 20
3y = 24

Divide both sides by 3.
3y / 3 = 24 / 3
y = 8

Plug this into the first equation to find x.
y - 5 = x
8 - 5 = x
3 = x

ANSWER: (3, 8)

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y - 2x = -6
5x - y = 9

Solve the first equation for y.
y - 2x + 2x = -6 + 2x
y = 2x - 6

Substitute y with 2x - 6 in the second equation.
5x - y = 9
5x - (2x - 6) = 9

Distribute.
5x - (2x) - (-6) = 9
5x - 2x + 6 = 9
3x + 6 = 9

Subtract 6 from both sides.
3x + 6 - 6 = 9 - 6
3x = 3

Divide both sides by 3.
3x / 3 = 3 / 3
x = 1

Plug this into the modified first equation.
y = 2x - 6
y = 2(1) - 6
y = 2 - 6
y = -4

ANSWER: (1, -4)

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3y + x = 2
y = x - 6

Substitute y with x - 6 in the first equation.
3y + x = 2
3(x - 6) + x = 2

Distribute.
3(x) + 3(-6) + x = 2
3x - 18 + x = 2
4x - 18 = 2

Add 18 to both sides.
4x - 18 + 18 = 2 + 18
4x = 20

Divide both sides by 4.
4x / 4 = 20 / 4
x = 5

Plug this into the second equation to find y.
y = x - 6
y = 5 - 6
y = -1

ANSWER: (5, -1)

John Said:

worksheets to graphically identify approximate solutions to systems of two linear equations.?

We Answered:

I'm not sure that you need any specific worksheet except for graph paper. If you're just looking for a way to approximate the solution of a system of equations, just graph the two lines and find the point of intersection. For easier problems, th intersection will be an easy point - at (1, 3) or at (-5, 2) for example. Otherwise, the intersection will be somewhere fractional, and you'll have to approximate the answers as (1.5, 3.5) for example.

Monica Said:

What does the graph of a system of linear equations look like if the product of the slopes of the lines is -1?

We Answered:

They will be perpendicular to each other...if one line has a slope of 3 then the other has a slope of -1/3....this is also a condition to check if 2 lines a perpendicular...the product of the slopes HAS to be =to -1 if they are to be perpendicular...
On the other hand if they are parallel their slopes are equal...

Fred Said:

Simple Algebra Need Help: Writing Linear Equations?

We Answered:

x-intercept 4 means (4, 0) is the point.

y-intercept - 2 means (0, - 2) is the point.


Calculate slope m = rise/run

m = (- 2 - 0)/(0 - 4) = - 2/(- 4) = 1/2


Using slope-intercept form y = mx + b

y = (1/2)x - 2

Jeffery Said:

linear equations in two variables? y = x - 5?

We Answered:

your question isn't complete. what are you supposed to do wth the equation?