17) solve this linear system using the method of substitution.
2y-x=-10
y= -3/2x-1
20) simplify then solve by substitution
2(x-4)+y=6
3x-2(y-3)=13
just need help with these 2.
2(x-4)+y=6
3x-2(y-3)=13
2 x - 8 + y = 6
3 x - 2 y + 6 = 13
2 x + y = 14
3 x -2y = 7
y = 14 - 2x use that
3 x - 2 (14-2x) = 7
3 x - 28 + 4 x = 7
7 x = 35 = 7*5
so
x = 5
go back and find y
17) To solve the linear system using the method of substitution:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Start with the second equation: y = (-3/2)x - 1.
Step 2: Substitute the expression obtained from step 1 into the other equation.
Substitute y = (-3/2)x - 1 into the first equation: 2((-3/2)x - 1) - x = -10.
Step 3: Simplify the equation obtained from step 2 and solve for the remaining variable.
Distribute 2: -3x - 2 - x = -10.
Combine like terms: -4x - 2 = -10.
Add 2 to both sides: -4x = -8.
Divide by -4: x = 2.
Step 4: Substitute the value of x back into one of the original equations to solve for the other variable.
Using the first equation: 2y - 2 = -10.
Add 2 to both sides: 2y = -8.
Divide by 2: y = -4.
Therefore, the solution to the linear system is x = 2 and y = -4.
20) To simplify and solve the linear system using substitution:
Step 1: Simplify both equations.
Starting with the first equation: 2(x - 4) + y = 6.
Expand the brackets: 2x - 8 + y = 6.
Step 2: Solve one of the equations for one variable in terms of the other variable.
Rearrange the first equation to isolate y: y = -2x + 14.
Step 3: Substitute the expression obtained from step 2 into the other equation.
Substitute y = -2x + 14 into the second equation: 3x - 2((-2x + 14) - 3) = 13.
Step 4: Simplify the equation obtained from step 3 and solve for the remaining variable.
Distribute -2: 3x + 4x - 26 + 6 = 13.
Combine like terms: 7x - 20 = 13.
Add 20 to both sides: 7x = 33.
Divide by 7: x = 33/7 = 4.71 (rounded to two decimal places).
Step 5: Substitute the value of x back into one of the original equations to solve for the other variable.
Using the first equation: 2(4.71 - 4) + y = 6.
Simplify: 2(0.71) + y = 6.
Multiply: 1.42 + y = 6.
Subtract 1.42 from both sides: y = 6 - 1.42 = 4.58 (rounded to two decimal places).
Therefore, the solution to the linear system is x = 4.71 and y = 4.58.
y= -3/2x-1
which I assume means
y = -(3/2)x - 1
so use that
2 [ -(3/2)x - 1 ] - x = -10
-3 x - 2 - x = -10
-4 x = -8
x = 2 etc