2x-y+=-9
3x-8y=-7
using the substitution method.
What's the answer?
for this
Georgette has n books. Jackie has half as many books. How many books does jackie have?
from the first equation,
y = 2x+9 (ignoring the spurious + sign)
substituting that into the second equation,
3x - 8(2x+9) = -7
3x - 16x - 72 = -7
-13x = 65
x = -5
so, y = -1
To solve the system of linear equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve equation "1" for x:
2x - y = -9
2x = y - 9
x = (y - 9)/2
Step 2: Substitute the expression from step 1 into the other equation.
We will substitute x = (y - 9)/2 into equation "2":
3x - 8y = -7
3((y - 9)/2) - 8y = -7
Step 3: Solve the resulting equation for the remaining variable.
Distribute 3 to ((y - 9)/2):
(3y - 27)/2 - 8y = -7
Multiply each term by 2 to remove the denominator:
3y - 27 - 16y = -14
Combine like terms:
-13y - 27 = -14
Add 27 to both sides of the equation:
-13y = -14 + 27
-13y = 13
Divide both sides by -13 to solve for y:
y = 13/-13
y = -1
Step 4: Substitute the value of y back into one of the original equations to find the value of x.
Using equation "1":
2x - y = -9
2x - (-1) = -9
2x + 1 = -9
Subtract 1 from both sides of the equation:
2x = -9 - 1
2x = -10
Divide both sides by 2 to solve for x:
x = -10/2
x = -5
Therefore, the solution to the system of equations is x = -5 and y = -1.