Solve this system of linear equations.
* Used the substitution method
3x - y = 8
4x - y = -15
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WORK
y = 3x - 8
4x - (3x - 8 ) = -15
4x - 3x + 8 = -15
x + 8 = -15
x = -7
3x - y = 8
3(-7) - y = 8
-21 - y = 8
-y = 29
y = -29
The solution of this linear equation is [ -7 , -29 ]
from your
x + 8 = -15
x = -15-8
x = -23
then
y = 3x-8
= 3(-23) - 8
= -77
check:
in #1
3x - y
= 3(-23) -(-77)
= -69 + 77 = 8 , check!
in #2:
4x - y
= 4(-23) - (-77)
= -92 + 77
= -15 , check!
x = -23 , y = -77
Can you please explain this? I don't quite understand it.
from your
x + 8 = -15
x = -15-8
x = -23
Thanks!
To get x alone on one side, you have to subtract 8 from both sides.
x + 8 - 8 = -15 - 8
Thank you
To solve this system of linear equations using the substitution method, follow these steps:
Step 1: Choose one equation and solve it for one variable in terms of the other variable.
In this case, let's solve the first equation for y:
3x - y = 8
=> y = 3x - 8
Step 2: Substitute the expression obtained in Step 1 into the other equation.
Replace y in the second equation with 3x - 8:
4x - (3x - 8) = -15
Step 3: Simplify and solve for x.
Distribute the negative sign:
4x - 3x + 8 = -15
x + 8 = -15
Subtract 8 from both sides:
x = -15 - 8
x = -23
Step 4: Substitute the value of x back into one of the original equations and solve for y.
Let's use the first equation:
3x - y = 8
3(-23) - y = 8
-69 - y = 8
Subtract -69 from both sides:
-y = 8 + 69
-y = 77
Multiply both sides by -1 to solve for y:
y = -77
Therefore, the solution to the system of linear equations is x = -23 and y = -77.