## what is y=4x-2 is equal to 3x+2y=-4? what is x and y?

y = 4x - 2

3x + 2y = -4

Substituting the value for y from the top equation into the bottom equation:

3x + 2(4x - 2) = -4

Solving:

Distributing the 2: 3x + 8x - 4 = -4

Adding the x-terms together: 11x - 4 = -4

Adding 4 to both sides: 11x = 0

Dividing by 11: x = 0

Substituting 0 for x into the first equation:

y = 4(0) - 2

y = -2

The solution to the set of equations is: x = 0, y = -2.

### Similar Problems from Web Search

## Properties of a straight line

### Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2*y-(4*x-2)=0

### Step 1 :

#### Pulling out like terms :

1.1 Pull out like factors :

2y - 4x + 2 = 2 • (y - 2x + 1)

#### Equation at the end of step 1 :

### Step 2 :

#### Equations which are never true :

2.1 Solve : 2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

#### Equation of a Straight Line

2.2 Solve y-2x+1 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-2x+1 = 0 and calculate its properties

#### Graph of a Straight Line :

#### Calculate the Y-Intercept :

Notice that when x = 0 the value of y is -1/1 so this line "cuts" the y axis at y=-1.00000

y-intercept = -1/1 = -1.00000#### Calculate the X-Intercept :

When y = 0 the value of x is 1/2 Our line therefore "cuts" the x axis at x= 0.50000

x-intercept = 1/2 = 0.50000#### Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -1.000 and for x=2.000, the value of y is 3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 3.000 - (-1.000) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 4.000/2.000 = 2.000### Geometric figure: Straight Line

- Slope = 4.000/2.000 = 2.000
- x-intercept = 1/2 = 0.50000
- y-intercept = -1/1 = -1.00000

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## 2 2y 4x

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Differential Equations - First Order Homogeneous Equations.

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