Name: _________________________________________________ Algebra 2: Systems of Equations
Topic D3: Matrix Solutions to Linear Systems | VERSION A Solve the following systems of equations using matrices. 1.
2.
3.
𝑥 + 𝑦 = −4 4.
4𝑥 − 2𝑦 = 2 2𝑥 − 𝑦 = −2 𝑦 = 3𝑥 − 1 How many solutions does this system of How many solutions does this system of equations have? equations have? If it has 1 solution, what is it? If it has 1 solution, what is it? 4𝑥 + 𝑦 = −13 5.
3𝑥 − 4𝑦 = −11 𝑥 + 𝑦 = −1 𝑦 = 2𝑥 + 4 How many solutions does this system of How many solutions does this system of equations have? equations have? If it has 1 solution, what is it? If it has 1 solution, what is it? 3𝑥 + 8𝑦 = 23 6.
𝑥 − 𝑦 + 2𝑧 = −1 4𝑥 − 5𝑦 = −32 𝑥 + 𝑦 + 𝑧 = 1 How many solutions does this system of 𝑥 − 𝑦 − 𝑧 = −7 equations have? How many solutions does this system of If it has 1 solution, what is it? equations have? If it has 1 solution, what is it? www.varsitylearning.com 1 Name: _________________________________________________ Algebra 2: Systems of Equations
Topic D3: Matrix Solutions to Linear Systems | VERSION A 7.
8.
𝑥 − 2𝑦 − 𝑧 = 4 9.
𝑥 + 2𝑦 = −5 2𝑥 + 𝑦 − 2𝑧 = −7 2𝑦 + 2𝑧 = −6 3𝑥 + 𝑦 − 𝑧 = −5 3𝑥 + 3𝑧 = −6 How many solutions does this system of How many solutions does this system of equations have? equations have? If it has 1 solution, what is it? If it has 1 solution, what is it? 𝑥 + 2𝑦 − 𝑧 = 2 1
2
2
5
1
6
1
4
10. − 𝑥 + 𝑦 = 29 2𝑥 − 2𝑦 − 𝑧 = 8 − 𝑥 + 𝑦 = 19 3𝑥 + 𝑦 + 2𝑧 = 1 How many solutions does this system of How many solutions does this system of equations have? equations have? If it has 1 solution, what is it? If it has 1 solution, what is it? www.varsitylearning.com 2 Name: _________________________________________________ Algebra 2: Systems of Equations
Topic D3: Matrix Solutions to Linear Systems | VERSION A Solve the following systems of equations using matrices. 1.
2.
3.
𝑥 + 𝑦 = −4 4.
4𝑥 − 2𝑦 = 2 2𝑥 − 𝑦 = −2 𝑦 = 3𝑥 − 1 How many solutions does this system of How many solutions does this system of equations have? One equations have? One If it has 1 solution, what is it? −2, −2 If it has 1 solution, what is it? 0, −1 4𝑥 + 𝑦 = −13 5.
3𝑥 − 4𝑦 = −11 𝑥 + 𝑦 = −1 𝑦 = 2𝑥 + 4 How many solutions does this system of How many solutions does this system of equations have? One equations have? One If it has 1 solution, what is it? −4, 3 If it has 1 solution, what is it? −1, 2 3𝑥 + 8𝑦 = 23 6.
𝑥 − 𝑦 + 2𝑧 = −1 4𝑥 − 5𝑦 = −32 𝑥 + 𝑦 + 𝑧 = 1 How many solutions does this system of 𝑥 − 𝑦 − 𝑧 = −7 equations have? One How many solutions does this system of If it has 1 solution, what is it? −3, 4 equations have? One If it has 1 solution, what is it? −3, 2, 2 www.varsitylearning.com 3 Name: _________________________________________________ Algebra 2: Systems of Equations
Topic D3: Matrix Solutions to Linear Systems | VERSION A 7.
8.
𝑥 − 2𝑦 − 𝑧 = 4 9.
𝑥 + 2𝑦 = −5 2𝑥 + 𝑦 − 2𝑧 = −7 2𝑦 + 2𝑧 = −6 3𝑥 + 𝑦 − 𝑧 = −5 3𝑥 + 3𝑧 = −6 How many solutions does this system of How many solutions does this system of equations have? One equations have? One If it has 1 solution, what is it? 0, −3, 2 If it has 1 solution, what is it? −1, −2, −1 𝑥 + 2𝑦 − 𝑧 = 2 2𝑥 − 2𝑦 − 𝑧 = 8 3𝑥 + 𝑦 + 2𝑧 = 1 1
2
2
5
1
6
1
4
10. − 𝑥 + 𝑦 = 29 − 𝑥 + 𝑦 = 19 How many solutions does this system of How many solutions does this system of equations have? One equations have? One If it has 1 solution, what is it? 2, −1, −2 If it has 1 solution, what is it? 6, 80 www.varsitylearning.com 4