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Solve the system substitution.
{-4.5x-2y=-12.5
{3.25x-y=-0.75
To solve this system by substitution, we will solve one equation for one variable and substitute it into the other equation.
Let's solve the second equation for y:
3.25x - y = -0.75
To isolate y, we can subtract 3.25x from both sides:
-y = -0.75 - 3.25x
To get rid of the negative sign, we will multiply both sides by -1:
y = 0.75 + 3.25x
Now that we have the value of y in terms of x, we can substitute it into the first equation:
-4.5x - 2(0.75 + 3.25x) = -12.5
Simplify:
-4.5x - 1.5 - 6.5x = -12.5
Combine like terms:
-11x - 1.5 = -12.5
To isolate x, we can add 1.5 to both sides:
-11x = -11
Divide both sides by -11:
x = 1
Now that we have the value of x, we can substitute it back into the equation for y:
y = 0.75 + 3.25(1)
Simplify:
y = 0.75 + 3.25
y = 4
Therefore, the solution to the system of equations is x = 1 and y = 4.
To solve the system of equations using substitution, we can solve one equation for one variable and substitute it into the other equation. Let's solve the second equation for y, and then substitute this expression into the first equation.
Given equations:
1) -4.5x - 2y = -12.5
2) 3.25x - y = -0.75
Step 1: Solve the second equation (eq. 2) for y.
First, let's isolate y:
3.25x - y = -0.75
-y = -0.75 - 3.25x
y = 3.25x + 0.75
Step 2: Substitute the expression for y from eq. 2 into eq. 1.
-4.5x - 2(3.25x + 0.75) = -12.5
-4.5x - 6.5x - 1.5 = -12.5
-11.5x - 1.5 = -12.5
Step 3: Simplify and solve for x.
-11.5x = -12.5 + 1.5
-11.5x = -11.0
x = -11.0 / -11.5
x = 0.957
Step 4: Substitute the value of x back into eq. 2 to find y.
y = 3.25(0.957) + 0.75
y = 3.110 + 0.75
y = 3.86
Therefore, the solution to the system of equations is:
x = 0.957 and y = 3.86.
To solve this system of equations by substitution, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the second equation for y in terms of x:
3.25x - y = -0.75
Subtract 3.25x from both sides:
-y = -3.25x - 0.75
Multiply both sides by -1 to isolate y:
y = 3.25x + 0.75
Step 2: Substitute the expression for y from Step 1 into the other equation.
Now, substitute 3.25x + 0.75 for y in the first equation:
-4.5x - 2(3.25x + 0.75) = -12.5
Step 3: Simplify and solve for x.
Expand the expression using the distributive property:
-4.5x - 6.5x - 1.5 = -12.5
Combine like terms:
-11x - 1.5 = -12.5
Add 1.5 to both sides:
-11x = -12.5 + 1.5
-11x = -11
Divide by -11:
x = -11 / -11
x = 1
Step 4: Substitute the value of x into one of the original equations to solve for y.
Let's substitute x = 1 into the second equation:
3.25(1) - y = -0.75
3.25 - y = -0.75
Subtract 3.25 from both sides:
-y = -0.75 - 3.25
-y = -4
Multiply by -1 to isolate y:
y = 4
Step 5: Check your answer.
Substitute x = 1 and y = 4 into both original equations to confirm that they satisfy both equations:
For the first equation: -4.5(1) - 2(4) = -12.5 (LHS = RHS)
For the second equation: 3.25(1) - 4 = -0.75 (LHS = RHS)
Therefore, the solution to the system of equations is x = 1 and y = 4.