systems of equations: substitution #1
use substitution to solve each system of equations.
1.
y = 6
-x + y = 2
(____ , ____)
2.
x = 5
3x - 2y = 9
(____ , ____)
3.
4x = -8
2x + 5y = 6
(____ , ____)
4.
y = -5x
6x + y = 2
(____ , ____)
5.
x = 9y
3y - 3x = 24
(____ , ____)
6.
y - x = -8
2x - 16 = y
(____ , ____)
7.
y = 3x + 1
y = 8x - 4
(____ , ____)
8.
x + y = 0
5x + 4y = 6
(____ , ____)
9.
2y = -2x + 6
x - 5y = -15
(____ , ____)
10.
5x + y = 2
20x + 3y = -4
(____ , ____)
11.
-8x + 2y = -14
4x - 6y = 22
(____ , ____)
12.
2x + 4y = -18
5x - 10y = -5
(____ , ____)

Question

Accepted Answer

# Explanation:
---
### Problem 1
## Step1: Substitute $y=6$ into 2nd equation
$-x + 6 = 2$
## Step2: Solve for $x$
$-x = 2 - 6 \implies -x = -4 \implies x=4$
# Answer (1):
$(4, 6)$

---
### Problem 2
## Step1: Substitute $x=5$ into 2nd equation
$3(5) - 2y = 9$
## Step2: Simplify and solve for $y$
$15 - 2y = 9 \implies -2y = 9-15 \implies -2y=-6 \implies y=3$
# Answer (2):
$(5, 3)$

---
### Problem 3
## Step1: Solve 1st equation for $x$
$x = \frac{-8}{4} = -2$
## Step2: Substitute $x=-2$ into 2nd equation
$2(-2) + 5y = 6$
## Step3: Solve for $y$
$-4 + 5y = 6 \implies 5y=10 \implies y=2$
# Answer (3):
$(-2, 2)$

---
### Problem 4
## Step1: Substitute $y=-5x$ into 2nd equation
$6x + (-5x) = 2$
## Step2: Simplify and solve for $x$
$x=2$
## Step3: Find $y$ using $y=-5x$
$y=-5(2)=-10$
# Answer (4):
$(2, -10)$

---
### Problem 5
## Step1: Substitute $x=9y$ into 2nd equation
$3y - 3(9y) = 24$
## Step2: Simplify and solve for $y$
$3y-27y=24 \implies -24y=24 \implies y=-1$
## Step3: Find $x$ using $x=9y$
$x=9(-1)=-9$
# Answer (5):
$(-9, -1)$

---
### Problem 6
## Step1: Substitute $y=2x-16$ into 1st equation
$(2x-16) - x = -8$
## Step2: Simplify and solve for $x$
$x-16=-8 \implies x=8$
## Step3: Find $y$ using $y=2x-16$
$y=2(8)-16=0$
# Answer (6):
$(8, 0)$

---
### Problem 7
## Step1: Set the two $y$ expressions equal
$3x + 1 = 8x - 4$
## Step2: Solve for $x$
$1+4=8x-3x \implies 5=5x \implies x=1$
## Step3: Find $y$ using $y=3x+1$
$y=3(1)+1=4$
# Answer (7):
$(1, 4)$

---
### Problem 8
## Step1: Rearrange 1st equation: $y=-x$
$y=-x$
## Step2: Substitute $y=-x$ into 2nd equation
$5x + 4(-x) = 6$
## Step3: Solve for $x$
$5x-4x=6 \implies x=6$
## Step4: Find $y$ using $y=-x$
$y=-6$
# Answer (8):
$(6, -6)$

---
### Problem 9
## Step1: Simplify 1st equation for $y$
$y=\frac{-2x+6}{2}=-x+3$
## Step2: Substitute $y=-x+3$ into 2nd equation
$x - 5(-x+3) = -15$
## Step3: Simplify and solve for $x$
$x+5x-15=-15 \implies 6x=0 \implies x=0$
## Step4: Find $y$ using $y=-x+3$
$y=-0+3=3$
# Answer (9):
$(0, 3)$

---
### Problem 10
## Step1: Rearrange 1st equation: $y=2-5x$
$y=2-5x$
## Step2: Substitute $y=2-5x$ into 2nd equation
$20x + 3(2-5x) = -4$
## Step3: Simplify and solve for $x$
$20x+6-15x=-4 \implies 5x=-10 \implies x=-2$
## Step4: Find $y$ using $y=2-5x$
$y=2-5(-2)=12$
# Answer (10):
$(-2, 12)$

---
### Problem 11
## Step1: Rearrange 1st equation for $y$
$2y=8x-14 \implies y=4x-7$
## Step2: Substitute $y=4x-7$ into 2nd equation
$4x - 6(4x-7) = 22$
## Step3: Simplify and solve for $x$
$4x-24x+42=22 \implies -20x=-20 \implies x=1$
## Step4: Find $y$ using $y=4x-7$
$y=4(1)-7=-3$
# Answer (11):
$(1, -3)$

---
### Problem 12
## Step1: Rearrange 1st equation for $x$
$2x=-18-4y \implies x=-9-2y$
## Step2: Substitute $x=-9-2y$ into 2nd equation
$5(-9-2y) -10y = -5$
## Step3: Simplify and solve for $y$
$-45-10y-10y=-5 \implies -20y=40 \implies y=-2$
## Step4: Find $x$ using $x=-9-2y$
$x=-9-2(-2)=-5$
# Answer (12):
$(-5, -2)$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1

Step1: Substitute $y=6$ into 2nd equation

Step2: Solve for $x$

Answer:

Problem 2

Step1: Substitute $x=5$ into 2nd equation

Step2: Simplify and solve for $y$