Lesson 7.4 Solve Linear Systems by Multiplying First Essential Question: How do you solve linear systems by multiplying first?

Before we start… Consider the linear system below. 2𝑥−3𝑦=−7 3𝑥+𝑦=−5 Multiply the second equation by 3. Is the new equation still equivalent to the original? Can you solve the system now?

The Elimination Method ** The goal of this method is to eliminate one of the variables by adding equations. STEP 1: Multiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables. STEP 2: Add the revised equations from Step 1. Combining like terms will eliminate one of the variables. Solve for the remaining variable. STEP 3: Substitute the value obtained in Step 2 into either of the original equations and solve for the other variable.

How do you solve linear systems by multiplying first? Multiply one or both of the equations by a constant so you can eliminate a variable. You’re looking for an LCM of the coefficients. Add or subtract the equations to eliminate one variable. Solve the resulting equation for the other variable. Substitute in either original equation to find the value of the eliminated variable. Write your answer as an ordered pair.

What if you have to multiply both equations first? If you have to multiply both equations by a constant first, you will use the least common multiple of the coefficients of one of the variables to determine what to multiply by.

Darlene is making a quilt that has alternating stripes of regular quilting fabric and satin fabric. Satin fabric costs $6 per yard and quilting fabric costs $4 per yard. She spends $76 on a total of 16 yards of the two fabrics at a fabric store. How many yards of quilting fabric and satin fabric did she use?

How do you solve linear systems by multiplying first?

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