Introduction
The SAT math section contains a few questions that deal with solving linear equations, but they’re often easy to solve. The SAT Math section includes linear equations in two different formats: as word problems and as grid-in questions. These problems are straightforward and require basic knowledge of algebraic functions. So, if you’re sitting down to take the test soon, here’s what you need to know about these types of SAT math problems.
How to Crack linear equations on the SAT Math?
1. Understand the Order of Operations
The order of operations is a set of rules that you need to follow when solving math problems. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
It’s important to know this because if you don’t follow the order of operations correctly then your answer will be wrong!
For example:
(2+3)^7 = 49
2. Use Substitution to Solve Linear Equations
Substitution is the most common method used to solve linear equations. You can use it in two ways: substitution by addition and substitution by subtraction to solve linear equations and crack high scores on SAT Quant section.
Substitution by Addition
· Substitution by Addition is used when you are given two equations with two variables, like this:
3x + 4y = 17
· To solve this equation, you need to make x and y have the same value on both sides of the equal sign (or else your answer will be wrong!). To do so, we’ll substitute x into one side of our equation with y as its value and then add 7 to both sides afterward:
3. Know how to solve linear equations with addition and subtraction
Addition and subtraction are two of the most fundamental operations in mathematics. It’s a simple idea: if you add two numbers, you get another number. In other words, if I have 2 apples and then I take one apple away from my collection, I still have 2 apples left over.
If we want to solve linear equations with variables on both sides (step 1), then we can use addition and subtraction as our tools!
For example:
x + 3 = y – 4
Let’s say that x=5 and y=-3…
4. Identify and solve the unknown variables in a system of equations
You will be asked to solve systems of equations in the SAT Math section. A system of two linear equations can be written as Ax + By = C and Dx + Ey = F, where A, B, C, and D are constants that do not equal 0.
• If you have more than two equations (for example three), then you should still treat each pair separately and solve them individually before combining your solutions into one solution for all variables.
• Identify which unknowns correspond with each other: In this case, we have x’s on both sides so they must be one variable; however, y is only found in one equation so it must represent another variable (as opposed to multiple).
• Solve each equation independently: We are going to try solving for x first by adding 3y – 4x = 6; then subtracting y from both sides of our first equation gives us 2x = 10-y which simplifies down into 2(10-y)/2 = 5(10 – y) which equals 100 – 50y or 50(10 – y)/2 which equals 25(-5y/10).
• Multiply both sides by 10(-5) since we’re dividing by negative numbers now (and make sure all your signs match up properly!) so our new equation looks like this:
25(-5)(10-y)/2 = 50(-5)(10-y)/2 = 100(-1)(10+4)-4(50)/-4(25)=100*0=0
[Read More: Expert Tips to get High Score on SAT]
5. Solve systems of linear equations graphically
• Use a graph to solve systems of linear equations.
• Draw a graph and label the x and y-axis.
• Mind points on your graph that represent the values given in each equation, then mark those points with dots or squares (x’s).
• Now find the slope of your line by finding two different points on your graph and using those coordinates to calculate their slopes (m1 and m2).
Finally, use these three pieces of information:
1) The slope of your line;
2) The point(s) representing solution(s);
3) Which side(s) of each original equation corresponds with which side(s) from another original equation (i.e., if “y = 2x + 5” was solved for x = 3 then this would mean that we know there exists some number k such that y = k * 3 + 5).
6. SAT math linear equation problems can be solved using basic math skills.
SAT math linear equation problems can be solved using basic math skills. To solve a linear equation, you must know the order of operations, which is:
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)
Once you know the order of operations, you will be able to solve any given problem by breaking it down into simple steps. For example, if there were an equation like
4x + 3y = 12
Linear equation problem-solving methods to help you prepare for your SAT test
You should have basic knowledge of how to solve linear equations using the following methods to improve your score on SAT math section:
1. Solving linear equations in SAT math
A linear equation is one that can be expressed as ax + b = c, where a, b, and c are real values.
There are several ways to solve linear equations. One method is substitution; another method is elimination and another method is addition and subtraction. Let’s take a look at each of these strategies individually:
• Substitution: In this method we substitute one side of the equation with another value so that only one variable remains on both sides (called “isolating” it). We then solve for this isolated variable using some kind of algebraic technique such as addition or subtraction (see below).
For example, let’s say we want to solve 2x + 5 = 9 – 4x for x:
• Substitute 4x for 2x by subtracting 4 from both sides of our equation: 2(4) – 10 = 9 – 8 = 1 –> 12 – 10 = 2 –> 2 + (-10) = 12 –> 12/2 = 6 –> 62=12 –> 66=36 …and therefore 36 is our solution!
2. What are the SAT linear equations questions like?
Linear equation questions are multiple-choice. You will be presented with three equations, and you must solve for one variable in each equation.
You’ll also be asked to solve for one variable and one number (e.g., “If x = 5 and y = 2, what is the value of z?”).
Finally, you may need to solve two linear equations at once — but we’ll get into that later!
3. How to solve linear equations on a grid method?
The grid method is a simple way to solve linear equations in the SAT Math section. To use this method, you need to draw a grid in your test booklet, then fill in all of the information given in each problem.
· First, draw a line across every row and column of your grid so that it covers all of your workspaces. You can use either a pencil or a pen—whichever works best for you!
· Next, label each side of your equation with letters instead of numbers (e.g., if 2x + 3 = 7x + 9, label them A and B). This will make things easier later on when we’re trying to figure out where everything should go on our grid!
[Read more: SAT vs Act, Which Test is Right for You?]
4. How to solve linear equations with a calculator method?
To solve linear equations on a calculator, you must first use the order of operations to evaluate the equation. The order of operations is:
· distribute any brackets or parentheses;
· Multiply or divide by numbers;
· Addition or subtraction (from left to right).
The second step is to plug in your values into the equation and solve for x. For example, let’s say we have this equation: 3x + 4 = 10. First, we would distribute our brackets (3x) and then add 4; this gives us 5x + 4 = 10 which can be simplified further by dividing both sides by 5: x = 2
5. How to solve linear equations by using the quadratic formula work?
To solve linear equations by using the quadratic formula, you need to know the basics of solving quadratics and how to use your calculator. The quadratic formula is:
ax^2 + bx + c = 0
where a, b, and c are real numbers and x is a variable that represents an unknown number in an equation. To solve for x, first, multiply both sides of this equation by -1:
(-a)(-1) = 1/4b^2 + 1/4c + 1/(4a)
Conclusion:
Linear equation solving is one of the most fundamental skills that you need to have mastered in order to do well on the SAT test with Expert Coaching. This article will go over how to solve linear equations and inequalities on the SAT by using the substitution method or graphing method.
