$$ x=2 y+1 $$ 5. Solve the following pairs of equations simultaneously using the substitution method. $$ \begin{array}{llll} ext { a. } y=2 x-5 & ext { b. } y=-x+4 & ext { c. } 4 x-5 y=17 & ext { d. } x=-5 y+1 \ 5 x-y=1 & 5 x=3 y & y=2 x-1 & 3 x+2 y=16\end{array} $$

Question

$$ x=2 y+1 $$ 5. Solve the following pairs of equations simultaneously using the substitution method. $$ \begin{array}{llll}	ext { a. } y=2 x-5 & 	ext { b. } y=-x+4 & 	ext { c. } 4 x-5 y=17 & 	ext { d. } x=-5 y+1 \ 5 x-y=1 & 5 x=3 y & y=2 x-1 & 3 x+2 y=16\end{array} $$

UpStudy AI · Accepted Answer

**a. Solve:**

$$
y = 2x - 5
$$

$$
5x - y = 1
$$

_Substitute_ $$ y = 2x - 5 $$ _into_ $$ 5x - y = 1 $$:

$$
5x - (2x - 5) = 1
$$

Simplify:

$$
5x - 2x + 5 = 1 \quad \Longrightarrow \quad 3x + 5 = 1
$$

Subtract 5 from both sides:

$$
3x = -4 \quad \Longrightarrow \quad x = -\frac{4}{3}
$$

_Substitute_ $$ x = -\frac{4}{3} $$ _back into_ $$ y = 2x-5 $$:

$$
y = 2\left(-\frac{4}{3}\right) - 5 = -\frac{8}{3} - 5 = -\frac{8}{3} - \frac{15}{3} = -\frac{23}{3}
$$

---

**b. Solve:**

$$
y = -x + 4
$$

$$
5x = 3y
$$

_Substitute_ $$ y = -x + 4 $$ _into_ $$ 5x = 3y $$:

$$
5x = 3(-x + 4) \quad \Longrightarrow \quad 5x = -3x + 12
$$

Add $$ 3x $$ to both sides:

$$
8x = 12 \quad \Longrightarrow \quad x = \frac{12}{8} = \frac{3}{2}
$$

_Substitute_ $$ x = \frac{3}{2} $$ _back into_ $$ y = -x + 4 $$:

$$
y = -\frac{3}{2} + 4 = -\frac{3}{2} + \frac{8}{2} = \frac{5}{2}
$$

---

**c. Solve:**

$$
4x - 5y = 17
$$

$$
y = 2x - 1
$$

_Substitute_ $$ y = 2x - 1 $$ _into_ $$ 4x - 5y = 17 $$:

$$
4x - 5(2x - 1) = 17
$$

Simplify:

$$
4x - 10x + 5 = 17 \quad \Longrightarrow \quad -6x + 5 = 17
$$

Subtract 5 from both sides:

$$
-6x = 12 \quad \Longrightarrow \quad x = -2
$$

_Substitute_ $$ x = -2 $$ _into_ $$ y = 2x - 1 $$:

$$
y = 2(-2) - 1 = -4 - 1 = -5
$$

---

**d. Solve:**

$$
x = -5y + 1
$$

$$
3x + 2y = 16
$$

_Substitute_ $$ x = -5y + 1 $$ _into_ $$ 3x + 2y = 16 $$:

$$
3(-5y + 1) + 2y = 16
$$

Simplify:

$$
-15y + 3 + 2y = 16 \quad \Longrightarrow \quad -13y + 3 = 16
$$

Subtract 3 from both sides:

$$
-13y = 13 \quad \Longrightarrow \quad y = -1
$$

_Substitute_ $$ y = -1 $$ _into_ $$ x = -5y + 1 $$:

$$
x = -5(-1) + 1 = 5 + 1 = 6
$$
**a.** $$ x = -\frac{4}{3} $$, $$ y = -\frac{23}{3} $$ **b.** $$ x = \frac{3}{2} $$, $$ y = \frac{5}{2} $$ **c.** $$ x = -2 $$, $$ y = -5 $$ **d.** $$ x = 6 $$, $$ y = -1 $$

5. Solve the following pairs of equations simultaneously using the substitution method.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

a.

b.

c.

d.

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