y = 3x + 6
y = -13x - 4
To find the value of x and y that satisfy both equations, we can set them equal to each other:
3x + 6 = -13x - 4
Now, let's solve for x:
Add 13x to both sides: 3x + 13x + 6 = -4
Combine like terms: 16x + 6 = -4
Subtract 6 from both sides: 16x = -10
Divide both sides by 16: x = -10/16 = -5/8
Now substitute the value of x back into one of the original equations to solve for y:
y = 3(-5/8) + 6
Simplify: y = -15/8 + 48/8 = 33/8
Therefore, the solution to the system of equations is x = -5/8 and y = 33/8.
To find the point of intersection between the two lines represented by the given equations, we need to solve the system of equations. Let's set the two equations equal to each other and solve for x:
3x + 6 = -13x - 4
First, let's simplify the equation by combining like terms:
3x + 13x = -4 - 6
16x = -10
Next, let's isolate x by dividing both sides of the equation by 16:
x = -10/16
Simplifying the right hand side:
x = -5/8
Now, substitute this value of x back into any of the original equations to find the value of y. Let's use the first equation:
y = 3(-5/8) + 6
Multiplying:
y = -15/8 + 6
To simplify the fraction, let's find a common denominator:
y = -15/8 + 48/8
Adding the fractions:
y = 33/8
Therefore, the point of intersection of the two lines is (-5/8, 33/8).
These are two linear equations in the form of y = mx + b, where m represents the slope of the line and b represents the y-intercept.
To solve these equations, we need to find the values of x and y that satisfy both equations simultaneously, meaning they lie on the intersection of the two lines.
We can do this by equating the two equations:
3x + 6 = -13x - 4
To isolate x, we need to move the terms with x to one side of the equation and the constant terms to the other side.
Adding 13x to both sides:
3x + 13x + 6 = -4
Combining like terms:
16x + 6 = -4
Next, we subtract 6 from both sides:
16x = -10
Finally, dividing both sides by 16:
x = -10/16 or x = -5/8
Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use the first equation:
y = 3(-5/8) + 6
Multiplying:
y = -15/8 + 6
Finding a common denominator:
y = -15/8 + 48/8
Adding:
y = 33/8
Therefore, the solution to the system of equations is x = -5/8 and y = 33/8.