Math Problem Statement

Use substitution

Solution

The image contains a set of linear equations, and you asked to solve them using substitution. I'll go through each pair of equations step by step.

1. Equations:

1. x+y=1\text{1. } -x + y = 1 2x+y=22x + y = -2

Step 1: Solve the first equation for yy: y=x+1y = x + 1

Step 2: Substitute y=x+1y = x + 1 into the second equation: 2x+(x+1)=22x + (x + 1) = -2 3x+1=23x + 1 = -2 3x=3x=13x = -3 \quad \Rightarrow \quad x = -1

Step 3: Substitute x=1x = -1 back into y=x+1y = x + 1: y=1+1=0y = -1 + 1 = 0

Solution for the first system: x=1,y=0x = -1, \quad y = 0

2. Equations:

2. 2x+2y=3\text{2. } 2x + 2y = 3 x4y=1x - 4y = -1

Step 1: Simplify the first equation by dividing by 2: x+y=32x + y = \frac{3}{2}

**Step 2: Solve for xx:

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Substitution Method

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9