Use the substitution method to solve the system y=−2x+1

Question

𝑦
=
−
2
𝑥
+
1
, −4x=−2y+10
−
4
𝑥
=
−
2
𝑦
+
10
.

Answer 1

To solve the system of equations using the substitution method, we start with the two equations given:

1. \( y = -2x + 1 \) (Equation 1)
2. \( -4x = -2y + 10 \) (Equation 2)

Now, we can substitute Equation 1 into Equation 2.

Step 1: Substitute \( y \) in Equation 2

From Equation 1, we know that:

\[ y = -2x + 1 \]

Now, substitute \( y \) in Equation 2:

\[ -4x = -2(-2x + 1) + 10 \]

Step 2: Simplify the equation

Now, simplify the right side:

\[ -4x = -2(-2x) - 2(1) + 10 \] \[ -4x = 4x - 2 + 10 \] \[ -4x = 4x + 8 \]

Step 3: Solve for \( x \)

Now, add \( 4x \) to both sides:

\[ -4x + 4x = 4x + 8 + 4x \] \[ 0 = 8x + 8 \]

Now, subtract 8 from both sides:

\[ -8 = 8x \]

Now, divide by 8:

\[ x = -1 \]

Step 4: Substitute \( x \) back to find \( y \)

Now that we have \( x = -1 \), we can substitute this back into Equation 1 to find \( y \):

\[ y = -2(-1) + 1 \] \[ y = 2 + 1 \] \[ y = 3 \]

Final Solution

So, the solution to the system of equations is:

\[ \boxed{(-1, 3)} \]