what is the solution to the following system of eaquations
y = x - 8
2x + y = 7
To solve this system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
1. Solve the first equation for y by adding 8 to both sides:
y = x - 8
2. Substitute the value of y in the second equation:
2x + (x - 8) = 7
3. Simplify the equation:
3x - 8 = 7
4. Add 8 to both sides:
3x = 15
5. Divide both sides by 3:
x = 5
6. Substitute the value of x into the first equation to find y:
y = 5 - 8
y = -3
7. The solution to the system of equations is x = 5 and y = -3.
Method 2: Elimination
1. Multiply the first equation by -1 to change the sign of both terms:
-y = -x + 8
2. Add the two equations together to eliminate the y term:
2x + y + (-x + 8) = 7
x + 8 = 7
3. Subtract 8 from both sides:
x = -1
4. Substitute the value of x into the second equation to find y:
2(-1) + y = 7
-2 + y = 7
5. Add 2 to both sides:
y = 9
6. The solution to the system of equations is x = -1 and y = 9.
Both methods yield the same solution: x = 5 and y = -3, or x = -1 and y = 9.
To find the solution to the given system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
Step 1: Solve one of the equations for one variable in terms of the other. Let's solve the first equation, y = x - 8, for y.
y = x - 8
Step 2: Substitute the expression for the variable y in the second equation with the value obtained in step 1.
2x + (x - 8) = 7
Step 3: Simplify the equation by combining like terms.
2x + x - 8 = 7
3x - 8 = 7
Step 4: Solve for x.
Add 8 to both sides:
3x = 15
Divide both sides by 3:
x = 5
Step 5: Substitute the value of x obtained in step 4 back into one of the original equations to solve for y. Let's use the first equation:
y = 5 - 8
y = -3
Therefore, the solution to the given system of equations is x = 5 and y = -3.
To solve the system of equations, we can use the method of substitution or elimination. In this case, let's use the method of substitution.
Step 1: Solve one of the equations for one variable in terms of the other variable.
Looking at the first equation, we have y = x - 8.
Step 2: Substitute the expression found in Step 1 into the other equation.
We substitute y = x - 8 into the second equation:
2x + (x - 8) = 7.
Step 3: Simplify and solve for the remaining variable.
2x + x - 8 = 7.
Combining like terms, we get:
3x - 8 = 7.
Adding 8 to both sides:
3x = 15.
Dividing both sides by 3:
x = 5.
Step 4: Substitute the value of x back into one of the original equations to find the value of the other variable.
Substituting x = 5 into y = x - 8:
y = 5 - 8.
y = -3.
Therefore, the solution to the system of equations is x = 5 and y = -3.