Solve the system of equations.
–9x+y=12
2x+4y= −28(1 point)
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
Step 1: Solve one equation for one variable.
From the first equation, we have:
-9x + y = 12
We can rearrange this equation to isolate y:
y = 12 + 9x
Step 2: Substitute the expression for y in the second equation.
Now, substitute the expression for y in the second equation:
2x + 4(12 + 9x) = -28
Step 3: Solve for x.
Expand the equation:
2x + 48 + 36x = -28
Combine like terms:
38x + 48 = -28
Subtract 48 from both sides:
38x = -76
Divide by 38:
x = -2
Step 4: Solve for y.
Now that we have the value of x, substitute it back into one of the original equations:
-9(-2) + y = 12
Simplify:
18 + y = 12
Subtract 18 from both sides:
y = -6
So the solution to the system of equations is x = -2 and y = -6.
To solve the system of equations, we can use either substitution or elimination method.
Using substitution:
- Solve one equation for one variable in terms of the other variable.
- Substitute the expression obtained for that variable into the other equation.
- Solve the resulting equation for the remaining variable.
- Substitute the value obtained back into one of the original equations to find the value of the other variable.
Here is how to use substitution to solve the system of equations:
- Solve the first equation for y:
y = 9x + 12
- Substitute this expression for y in the second equation:
2x + 4(9x + 12) = -28
- Simplify the equation by distributing 4:
2x + 36x + 48 = -28
- Combine like terms:
38x + 48 = -28
- Subtract 48 from both sides:
38x = -76
- Divide by 38:
x = -2
- Substitute x = -2 into the first equation to find y:
-9(-2) + y = 12
y = 12 + 18
y = 30
Therefore, the solution to the system of equations is:
x = -2 and y = 30.