**Solve Equations With 2 Variables** – Solve the system by substitution. y = 3x y = x – 2 Step 1 y = 3x Both equations are solved for y. y = x – 2 Step 2 y = x – 2 3x = x – 2 Substitute 3x for y in the second equation. Step 3 –x –x 2x = –2 2x = –2 x = –1 Solve for x. Subtract x on both sides and divide by 2.

Write one of the original equations. Step 4 y = 3x y = 3(–1) y = –3 Substitute -1 for x. Write the solution as an ordered pair. Step 5 (–1, –3) Check Substitutions (–1, –3) in both system equations. y = 3x –3 3(–1) –3 –3 y = x –2 –3 –1 – 2 –3 –3

## Solve Equations With 2 Variables

4 Check it out. Example 1a Solve the system by substitution. y = x + 3 y = 2x + 5 Step 1 y = x + 3 y = 2x + 5 Both equations are solved for y. Step 2 2x + 5 = x + 3 y = x + 3 Substitute 2x + 5 for y in the first equation. –x–5 –x–5 x = –2 Step 3 2x + 5 = x + 3 Solve for x. Subtract x and 5 from both sides.

#### Ways To Solve Systems Of Equations

Solve the system by substitution. Write one of the original equations. Step 4 y = x + 3 y = –2 + 3 y = 1 Replace –2 in x. Step 5 (–2, 1) Write the solution as an ordered pair.

Solve the system by substitution. y = x + 1 4x + y = 6 The first equation is solved for y. Step 1 y = x + 1 Step 2 4x + y = 6 4x + (x + 1) = 6 Substitute x + 1 for y in the second equation. 5x + 1 = 6 Shortened. Solve for x. Step 3 –1 –1 5x = 5 x = 1 5x = 5 Subtract 1 for both sides. Divide both sides by 5.

Write one of the original equations. Step 4 y = x + 1 y = 1 + 1 y = 2 Substitute 1 in x. Write the solution as an ordered pair. Step 5 (1, 2) Check Substitution (1, 2) in both equations of the system. y = x + 1 2 2 4x + y = 6 4(1) 6 6

## Easy Guide On How To Solve Equations With Fractions

8 Check it out. Example 1b Solve the system by substitution. x = 2y – 4 x + 8y = 16 Step 1 x = 2y – 4 The first equation is solved for x. (2y – 4) + 8y = 16 x + 8y = 16 Step 2 Substitute 2y – 4 for x in the second equation. Step 3 10y – 4 = 16 Shorten. Then solve for y. 10y = 20 Add 4 to both sides. 10y = Divide both sides by 10. y = 2

Solve the system by substitution. Step 4 x + 8y = 16 Write one of the original equations. x + 8(2) = 16 Replace 2 for y. x + 16 = 16 Shortened. x = 0 – 16 -16 Subtract 16 from both sides. Write the solution as an ordered pair. Step 5 (0, 2)

10 Check it out. Example 1c Solve the system by substitution. 2y + x = –4 x = y + 5 Step 1 2y + y + 5 = –4 Combine the same terms. 3y + 5 = –4 Subtract 5 on each side. 3y = -9 Divide each side by 3. y = -3 Write one of the original equations. Step 2 x = y + 5 x = (-3) + 5 Substitute -3 for y. x = 2 Step 3 (2, -3)

## Linear Systems With Two Variables And Their Solutions

Solve the system by substitution. x + 2y = –1 x – y = 5 Step 1 x + 2y = –1 Solve the first equation of x by subtracting 2y from both sides. −2y −2y x = –2y – 1 Step 2 x – y = 5 (–2y – 1) – y = 5 Substitute –2y – 1 for x in the second equation. –3y – 1 = 5 Shortened.

12 Example 1C Continue Step 2 –3y – 1 = 5 Solve for y. +1 +1 –3y = 6 Add 1 to both sides. –3y = 6 –3 –3 y = –2 Divide both sides by –3. Step 3 x – y = 5 Write one of the original equations. x – (–2) = 5 x + 2 = 5 Substitute –2 for y. –2 –2 x = 3 Subtract 2 for both sides. Write the solution as an ordered pair. Step 4 (3, -2)

13 Sometimes you replace an expression with a variable with a coefficient. In this situation, you can use the distributive property when addressing the second variable.

## Unit 2: Equations And Inequalities With Variables On Both Sides

Y = -6x + 11 Solve by substitution. 3x + 2y = –5 3x + 2(–6x + 11) = –5 3x + 2y = –5 Step 1 Substitute –6x + 11 into y in the second equation. 3x + 2(–6x + 11) = –5 Divide the expression in brackets by 2.

15 Example 2 Continue y + 6x = 11 Solve that way. 3x + 2y = –5 Step 2 3x + 2(–6x) + 2(11) = –5 Reduce. Solve for x. 3x – 12x + 22 = –5 –9x + 22 = –5 –9x = –27 – 22 –22 Subtract both sides by 22. –9x = –27 – –9 Divide both sides by –9. x = 3

16 Example 2 Continue y + 6x = 11 Solve by substitution. 3x + 2y = –5 Write one of the original equations. Step 3 y + 6x = 11 y + 6(3) = 11 Substitute 3 for x. y + 18 = 11 Shorten. –18 –18 y = –7 Subtract 18 from each side. Step 4 (3, –7) Write the solution as an ordered pair.

### Teaching Linear Equations In Math

17 Check it out. Example 2 y = 2x + 8 Solve by substitution. 3x + 2y = 9 3x + 2(2x + 8) = 9 3x + 2y = 9 Step 1 Substitute 2x + 8 for y in the second equation. 3x + 2(2x + 8) = 9 Divide the expression in brackets by 2.

–2x + y = 8 Solve by substitution. 3x + 2y = 9 Step 2 3x + 2(2x) + 2(8) = 9 Reduction. Solve for x. 3x + 4x = 9 7x = 9 7x = –7 –16 –16 Subtract both sides by 16. 7x = –7 Divide both sides by 7. x = -1

–2x + y = 8 Solve by substitution. 3x + 2y = 9 Write one of the original equations. Step 3 -2x + y = 8 -2(–1) + y = 8 Substitute -1 for x. y + 2 = 8 Shorten. –2 –2 y = 6 Subtract 2 on each side. Step 4 (–1, 6) Write the solution as an ordered pair.

## Pair Of Linear Equation In Two Variables: Methods, Solved Examples & Faqs

20 Let’s take a look. Example 1c Solve the system by substitution. 2x + y = 1 x – y = –7 Solve the second equation of x by adding y to each side. Step 1 x – y = –7 + y + y x = y – 7 2(y – 7) + y = 1 x = y – 7 Step 2 Replace x with y – 7 in the first equation. 2(y – 7) + y = 1 Divisible by 2. 2y – 14 + y = 1

Solve the system by substitution. Step 3 2y – 14 + y = 1 Combine the same terms. 3y – 14 = 1 3y = 15 Add 14 to each side. Divide each side by 3 y = 5 Step 4 X – y = –7 Write one of the original equations. x – (5) = –7 Replace 5 for y. x – 5 = – 7

Solve the system by substitution. Step 5 x – 5 = –7 Subtract 5 for both sides. x = -2 Step 6 (-2, 5) Write the solution as an ordered pair.

## New Algorithm Breaks Speed Limit For Solving Linear Equations

Jenna is deciding between two cell phone plans. The first plan has a $50 subscription fee and it costs $20 per month. The second plan has a $30 subscription and costs $25 per month. After how many months will the total costs be the same? How much will the cost be? If Jenna signs a 1-year contract, which plan will be cheaper? Explain. Write an equation for each option. Let t be the total amount paid and m the number of months.

24 Example 2 Next Total registration fee payment paid for each month. is plus Option 1 t = $50 + $20 m Option 2 t = $30 + $25 m Step 1 t = m t = m Both equations are solved for t. Step 2 m = m Substitute t for m in the second equation.

25 Example 2 Next Step 3 m = m Solve