-x-4y=-14 2x=y+1
Let's look at your two equations.
-x - 4y = -14
2x = y + 1
Let's solve the second equation for y:
y = 2x - 1
Now let's substitute (2x - 1) for y in the first equation:
-x - 4(2x - 1) = -14
-x - 8x + 4 = -14
-9x + 4 = -14
-9x = -18
x = 2
Substitute 2 for x in the second equation and solve for y:
2(2) = y + 1
4 = y + 1
y = 3
Check these values with the original equations. It always helps to check your work!
I hope this will help.
To solve the system of equations, we can use the method of substitution.
First, let's solve the second equation for y.
2x = y + 1
To isolate y, we subtract 1 from both sides:
2x - 1 = y
Now that we have the expression for y, we can substitute it into the first equation.
-x - 4y = -14
Replacing y with 2x - 1:
-x - 4(2x - 1) = -14
Simplifying the equation:
-x - 8x + 4 = -14
Combining like terms:
-9x + 4 = -14
To isolate x, we subtract 4 from both sides:
-9x = -18
Dividing both sides by -9:
x = 2
Now that we have the value of x, we can substitute it back into the second equation to find y.
2(2) = y + 1
Simplifying the equation:
4 = y + 1
Subtracting 1 from both sides:
3 = y
So the solution to the system of equations is x = 2 and y = 3.
To check our solution, we can substitute these values into the original equations:
First equation:
-x - 4y = -14
-(2) - 4(3) = -14
-2 - 12 = -14
-14 = -14
Second equation:
2x = y + 1
2(2) = 3 + 1
4 = 4
The values of x = 2 and y = 3 satisfy both equations, so our solution is correct.