solve following system of equations
y = 3x + 6
y = -13x - 4
To solve the system of equations y = 3x + 6 and y = -13x - 4, we can set the right sides of the equations equal to each other:
3x + 6 = -13x - 4
Next, let's add 13x to both sides and subtract 6 from both sides to isolate the variable x:
3x + 13x + 6 - 6 = -13x + 13x - 4 - 6
16x = -10
Now, divide both sides by 16 to solve for x:
(16x) / 16 = (-10) / 16
x = -10/16
Simplifying the fraction gives:
x = -5/8
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation y = 3x + 6:
y = 3(-5/8) + 6
y = -15/8 + 48/8
y = 33/8
Therefore, the solution to the system of equations is x = -5/8 and y = 33/8.
To solve the given system of equations, y = 3x + 6 and y = -13x - 4, we can use the method of substitution or elimination. Let's use the substitution method in this case.
Step 1: Start by equating the two equations:
3x + 6 = -13x - 4
Step 2: Now, solve the equation for x:
3x + 13x = -4 - 6
16x = -10
Step 3: Divide both sides of the equation by 16 to isolate x:
x = -10/16
x = -5/8 or -0.625
Step 4: Now that we have a value for x, substitute it back into either of the original equations to find the corresponding value of y. Let's substitute it into the first equation:
y = 3(-5/8) + 6
y = (-15/8) + 6
y = (-15/8) + (48/8)
y = 33/8 or 4.125
So, the solution to the given system of equations is x = -5/8 and y = 33/8 or approximately x = -0.625 and y = 4.125.
To solve the given system of equations:
Step 1: Set the two equations equal to each other since they both equal y:
3x + 6 = -13x - 4
Step 2: Add 13x to both sides of the equation to get the x terms on the left side:
16x + 6 = -4
Step 3: Subtract 6 from both sides to isolate the x term:
16x = -10
Step 4: Divide both sides by 16 to solve for x:
x = -10/16
Simplifying the fraction:
x = -5/8
Step 5: Substitute the value of x found in step 4 back into either of the original equations to find y. Let's use the first equation:
y = 3(-5/8) + 6
Step 6: Simplify the equation further:
y = -15/8 + 48/8
Combining the fractions:
y = 33/8
So the solution to the system of equations is x = -5/8 and y = 33/8.